PRICING SUPPLEMENT NO. 32                                       Rule 424(b)(3)
DATED:   August 31, 2004                                   File No. 333-109793
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)

                                 $10,668,950,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount: $5,000,000     Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 9/22/2004   Fixed Rate Notes [ ]    Certificated Notes [ ]

Maturity Date: 9/22/2011         CUSIP#: 073928G64

Option to Extend Maturity:
                                 No  [x]
                                 Yes [ ]  Final Maturity Date:

Minimum Denominations:  $100,000, increased in multiples of $10,000

                                              Optional           Optional
                         Redemption           Repayment          Repayment
   Redeemable On          Price(s)             Date(s)           Price(s)
   -------------       --------------       -------------      ------------

         *                    *                  N/A                 N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                     Maximum Interest Rate:  N/A

[   ] Commercial Paper Rate              Minimum Interest Rate:  0.00%

[   ] Federal Funds Effective Rate

[   ] Federal Funds Open Rate            Interest Reset Date(s):  **

[   ] Treasury Rate                      Interest Reset Period:  Quarterly

[   ] LIBOR Reuters                      Interest Payment Date(s):  ***

[ x ] LIBOR Telerate +

[   ] Prime Rate

[   ] CMT Rate

Interest Rate: Cliquet Inverse           Interest Payment Period:  Quarterly
               Floating Rate+
               See Annex A

Index Maturity:  Six Months              Interest Determination Date(s): 5th
                                         London Banking Day prior to but not
                                         including the last day of the
                                         immediately preceding Interest Payment
                                         Period, and for purposes of this
                                         provision only, without giving effect
                                         to the Business Day Convention (as
                                         defined in Annex A below)

Spread (plus or minus):  N/A             Day Count Basis:  360-day year of
                                                           twelve
                                                           30-day months

*  Commencing December 22, 2004 and on each Interest Payment Date thereafter
   until Maturity, the Notes may be called in whole at par at the option of the
   Company on five Business Days' notice. For purposes of this provision only,
   "Business Day" means any day that is not a Saturday or Sunday, and that is
   neither a legal holiday nor a day on which banking institutions or trust
   companies in New York City are authorized or obligated by law to close.

** Commencing December 22, 2004 and on the 22nd of each March, June, September
   and December prior to Maturity.

***Commencing December 22, 2004 and on the 22nd of each March, June, September
   and December thereafter, including the maturity date.

                  CERTAIN US FEDERAL INCOME TAX CONSIDERATIONS

      The following discussion summarizes certain US federal income tax
consequences of the purchase, beneficial ownership and disposition of the
Cliquet Inverse Floating Rate Notes (the "Notes"). This discussion supplements
the section captioned "Certain US Federal Income Tax Considerations" in the
Prospectus Supplement dated November 17, 2003. This summary deals only with a
beneficial owner of a Note that is:

      o     an individual who is a citizen or resident of the United States for
            US federal income tax purposes;

      o     a corporation (or other entity that is treated as a corporation for
            US federal tax purposes) that is created or organized in or under
            the laws of the United States or any State thereof (including the
            District of Columbia);

      o     an estate whose income is subject to US federal income taxation
            regardless of its source; or

      o     a trust if a court within the United States is able to exercise
            primary supervision over its administration, and one or more United
            States persons have the authority to control all of its substantial
            decisions (each, a "US Holder").

      If a partnership (or other entity that is treated as a partnership for US
federal tax purposes) is a beneficial owner of Notes, the treatment of a partner
in the partnership will generally depend upon the status of the partner and upon
the activities of the partnership. A beneficial owner of Notes that is a
partnership, and partners in such a partnership, should consult their tax
advisors about the US federal income tax consequences of holding and disposing
of the Notes.

      This discussion is based on interpretations of the Internal Revenue Code
of 1986, as amended (the "Code"), regulations issued there under, and rulings
and decisions currently in effect (or in some cases proposed), all of which are
subject to change. Any such change may be applied retroactively and may
adversely affect the federal income tax consequences described in this Pricing
Supplement. This summary addresses only US Holders that purchase Notes at
initial issuance and beneficially own such Notes as capital assets and not as
part of a "straddle," "hedge," "synthetic security" or a "conversion
transaction" for federal income tax purposes, or as part of some other
integrated investment. This summary does not discuss all of the tax consequences
that may be relevant to particular investors or to investors subject to special
treatment under the federal income tax laws (such as S corporations, banks,
thrifts, other financial institutions, insurance companies, mutual funds, small
business investment companies, tax-exempt organizations, retirement plans, real
estate investment trusts, regulated investment companies, securities dealers or
brokers, traders in securities electing mark to market treatment, investors
whose functional currency is not the US dollar, persons subject to the
alternative minimum tax, and former citizens or residents of the United States),
and this summary does not discuss the tax consequences under the laws of any
foreign, state or local taxing jurisdictions. Accordingly, prospective investors
are urged to consult their tax advisors with respect to the federal, state and
local tax consequences of investing in the Notes, as well as any consequences
arising under the laws of any other taxing jurisdiction to which they may be
subject.

      PROSPECTIVE PURCHASERS OF NOTES SHOULD CONSULT THEIR TAX ADVISORS AS TO
THE FEDERAL, STATE, LOCAL, AND OTHER TAX CONSEQUENCES TO THEM OF THE PURCHASE,
OWNERSHIP AND DISPOSITION OF NOTES.

Federal Income Tax Treatment of US Holders.

      General

      There are no regulations, rulings or other authorities addressing the
federal income tax treatment of debt instruments with terms that are
substantially similar to the Notes, and therefore the federal income tax
treatment of the Notes is subject to some uncertainty.

      Under certain Treasury regulations addressing the timing and character of
income, gain, loss and deduction in respect of debt instruments (the "the OID
regulations"), for purposes of determining the yield and maturity of a debt
instrument, an issuer is generally deemed to exercise a call option in a manner
that minimizes the yield on the debt instrument. The OID regulations do not
indicate how this rule is applied to debt instruments, such as the Notes, that
provide for an inverse floating rate of interest and are callable at par. We
intend to take the position that for purposes of applying this rule, the yield
on the Notes should be calculated assuming each Quarterly Coupon is computed
based on the 6 Month USD LIBOR rate in effect on the date the Notes are issued.
Based on this assumption, our yield would be minimized by exercising our call on
December 22, 2004 and therefore, for purposes of the OID regulations, the Notes
would be treated as bearing interest at the initial Interest Rate and having a
maturity of three months. This assumption has been made solely for federal
income tax purposes in order to comply with the OID regulations. This assumption
does not necessarily reflect our expectations regarding the actual yield on the
Notes, nor is it an indication of our intention regarding whether or not to call
the Notes at any time.

      Under this position, the Quarterly Coupon on a Note for the initial
Interest Payment Period will be taxable to a US Holder as ordinary interest
income at the time it accrues or is received in accordance with the US Holder's
normal method of accounting for tax purposes. If we do not call the Notes on
December 22, 2004, solely for purposes of the OID regulations, the Notes would
be deemed to be retired and reissued at the end of the initial Interest Payment
Period and at the end of each subsequent Interest Payment Period. In this event,
a US Holder would not recognize gain or loss in respect of such deemed
retirement and reissuance and the Quarterly Coupon for the subsequent Interest
Payment Period would be taxable to the US Holder as ordinary interest income at
the time it accrues or is received in accordance with the US Holder's normal
method of accounting for tax purposes calculated based upon the 6 Month USD
LIBOR rate in effect at that time.

      Sale, Exchange, Redemption, Repayment or Other Disposition of the Notes

      Under the approach described above, upon the disposition of a Note by
sale, exchange, redemption (if we exercise our call right or otherwise),
repayment or other disposition, a US Holder will generally recognize taxable
gain or loss equal to the difference, if any, between (i) the amount realized on
the disposition (other than amounts attributable to accrued but unpaid interest,
which would be treated as such) and (ii) the US Holder's adjusted tax basis in
the Note. A US Holder's adjusted tax basis in a Note generally will equal the
cost of the Note (net of accrued interest) to the US Holder. Capital gains of
individual taxpayers from the sale, exchange, redemption, repayment or other
disposition of a Note held for more than one year may be eligible for reduced
rates of taxation. The deductibility of a capital loss realized on the sale,
exchange, redemption, repayment or other disposition of a Note is subject to
limitations.

      Alternative Treatment

      As mentioned above, there are no regulations, rulings or other authorities
addressing the federal income tax treatment of debt instruments with terms that
are substantially similar to the Notes, and therefore the federal income tax
treatment of the Notes is subject to some uncertainty. Accordingly, other
treatments of the Notes are possible. For example, in the event that we are not
deemed to exercise our right to call the Notes for purposes of the OID
regulations on December 22, 2004, it is possible that the Notes could be treated
as "contingent payment debt instruments" for federal income tax purposes. If the
Notes were treated as contingent payment debt instruments for federal income tax
purposes, the timing and character of income with respect to the Notes would be
significantly affected. For example, a US Holder would be required to include in
income in each year an amount equal to the "comparable yield" of the Notes,
which is generally equal to the yield at which we would issue a noncontingent
debt instrument with terms and conditions similar to the Notes. In addition, a
"projected payment schedule" would be computed as of the Original Issue Date
that would produce the comparable yield. Furthermore, any gain realized on the
maturity date or upon an earlier call, sale, exchange or other disposition of
the Notes would generally be treated as ordinary income, and any loss realized
on the maturity date or upon an earlier call, sale, exchange or other
disposition of the Notes would be treated as ordinary loss to the extent of
interest included as income in the current or previous taxable years by the US
Holder in respect of the Notes, and capital loss thereafter. The federal income
tax treatment of contingent payment debt instruments is summarized in the
Prospectus Supplement dated November 17, 2003 under the caption "Certain US
Federal Income Tax Considerations - Contingent Payment Debt Instruments."

Disclosure Requirements for Certain US Holders Recognizing Significant Losses.

      A US Holder that is an individual or a partnership with one or more
noncorporate partners that claims a loss of $2 million or more in a taxable year
or $4 million or more in any combination of taxable years in respect of a Note
may be subject to certain disclosure requirements for "reportable transactions."
Prospective investors should consult their own tax advisors concerning any
possible disclosure obligation with respect to the Notes.

Information Reporting and Backup Withholding.

      Information reporting will apply to certain payments on a Note (including
interest and OID) and proceeds of the sale of a Note held by a US Holder that is
not an exempt recipient (such as a corporation). Backup withholding may apply to
payments made to a US Holder if (a) the US Holder has failed to provide its
correct taxpayer identification number on IRS Form W-9, (b) we have been
notified by the IRS of an underreporting by the US Holder (underreporting
generally refers to a determination by the IRS that a payee has failed to
include in income on its tax return any reportable dividend and interest
payments required to be shown on a tax return for a taxable year), or (c) we
have been notified by the IRS that the tax identification number provided to the
IRS on an information return does not match IRS records or that the number was
not on the information return.

      Backup withholding is not an additional tax and may be refunded (or
credited against your US federal income tax liability, if any), provided, that
certain required information is furnished. The information reporting
requirements may apply regardless of whether withholding is required.

THE PRECEDING DISCUSSION IS ONLY A SUMMARY OF CERTAIN OF THE TAX IMPLICATIONS OF
AN INVESTMENT IN NOTES. PROSPECTIVE PURCHASERS ARE URGED TO CONSULT WITH THEIR
OWN TAX ADVISORS PRIOR TO INVESTING TO DETERMINE THE TAX IMPLICATIONS OF SUCH
INVESTMENT IN LIGHT OF EACH SUCH INVESTOR'S PARTICULAR CIRCUMSTANCES.


The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.




                                     Annex A
                                     -------

                          Cliquet Inverse Floating Rate

+  The Interest Rate for each Interest Payment Period shall be determined by the
Calculation Agent in accordance with the following:




------------------------------------------------------------------------------------------
             Interest Payment Period                         Quarterly Coupon
------------------------------------------------------------------------------------------
                                               
For the Interest Payment Period from and              10.00% (initial Interest Rate)
including September 22, 2004 to but excluding
December 22, 2004
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 2.00% - 6
including December 22, 2004 to but excluding      Month USD LIBOR
March 22, 2005
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 2.00% - 6
including March 22, 2005 to but excluding June    Month USD LIBOR
22, 2005
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 2.50% - 6
including June 22, 2005 to but excluding          Month USD LIBOR
September 22, 2005
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 2.50% - 6
including September 22, 2005 to but excluding     Month USD LIBOR
December 22, 2005
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 3.00% - 6
including December 22, 2005 to but excluding      Month USD LIBOR
March 22, 2006
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 3.00% - 6
including March 22, 2006 to but excluding June    Month USD LIBOR
22, 2006
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 3.50% - 6
including June 22, 2006 to but excluding          Month USD LIBOR
September 22, 2006
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 3.50% - 6
including September 22, 2006 to but excluding     Month USD LIBOR
December 22, 2006
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 4.00% - 6
including December 22, 2006 to but excluding      Month USD LIBOR
March 22, 2007
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 4.00% - 6
including March 22, 2007 to but excluding June    Month USD LIBOR
22, 2007
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 4.50% - 6
including June 22, 2007 to but excluding          Month USD LIBOR
September 22, 2007
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 4.50% - 6
including September 22, 2007 to but excluding     Month USD LIBOR
December 22, 2007
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 5.00% - 6
including December 22, 2007 to but excluding      Month USD LIBOR
March 22, 2008
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 5.00% - 6
including March 22, 2008 to but excluding June    Month USD LIBOR
22, 2008
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 5.50% - 6
including June 22, 2008 to but excluding          Month USD LIBOR
September 22, 2008
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 5.50% - 6
including September 22, 2008 to but excluding     Month USD LIBOR
December 22, 2008
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 6.00% - 6
including December 22, 2008 to but excluding      Month USD LIBOR
March 22, 2009
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 6.00% - 6
including March 22, 2009 to but excluding June    Month USD LIBOR
22, 2009
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 6.50% - 6
including June 22, 2009 to but excluding          Month USD LIBOR
September 22, 2009
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 6.50% - 6
including September 22, 2009 to but excluding     Month USD LIBOR
December 22, 2009
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 7.00% - 6
including December 22, 2009 to but excluding      Month USD LIBOR
March 22, 2010
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 7.00% - 6
including March 22, 2010 to but excluding June    Month USD LIBOR
22, 2010
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 7.50% - 6
including June 22, 2010 to but excluding          Month USD LIBOR
September 22, 2010
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 7.50% - 6
including September 22, 2010 to but excluding     Month USD LIBOR
December 22, 2010
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 8.00% - 6
including December 22, 2010 to but excluding      Month USD LIBOR
March 22, 2011
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 8.00% - 6
including March 22, 2011 to but excluding June    Month USD LIBOR
22, 2011
-------------------------------------------------------------------------------------------
For the Interest Payment Period from and          Previous Quarterly Coupon + 8.00% - 6
including June 22, 2011 to but excluding          Month USD LIBOR
September 22, 2011
------------------------------------------------------------------------------------------



      Previous Quarterly Coupon means the Interest Rate for the preceding
Interest Payment Period.

      With respect to any Interest Payment Period, 6 month USD LIBOR shall be
USD LIBOR set in arrears with a designated maturity of 6 months as published on
Telerate page 3750 on the fifth London Banking Day prior to but not including
the last day of the immediately preceding Interest Payment Period. For any
Interest Payment Period where 6 month USD LIBOR sets below 0.00%, 6 month USD
LIBOR shall be deemed to be 0.00% for that Interest Payment Period.

      If any Interest Reset Date would otherwise be a day that is not a Business
Day, such Interest Reset Date shall be postponed to the next succeeding day that
is a Business Day, except that if such Business Day is in the next succeeding
calendar month, such Interest Reset Date shall be the next preceding Business
Day (any such adjustment being referred to as the "Business Day Convention").
For purposes of determining an Interest Reset Date, "Business Day" means any day
that is not a Saturday or Sunday, and that is neither a legal holiday nor a day
on which banking institutions or trust companies in New York City are authorized
or obligated by law to close and which is also a London Banking Day. A "London
Banking Day" means any day on which dealings in deposits in U.S. dollars are
transacted in the London interbank market.