PRICING SUPPLEMENT NO. 21                                         Rule 424(b)(3)
DATED: March 1, 2006                                         File No. 333-121744

(To Prospectus dated February 2, 2005,
and Prospectus Supplement dated February 2, 2005)

                                 $12,410,781,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount: $385,000,000   Floating Rate Notes [x]    Book Entry Notes [x]
Original Issue Date: 03/06/2006  Fixed Rate Notes [_]     Certificated Notes [_]
Maturity Date: 03/06/2008        CUSIP#: 073928N82
Option to Extend Maturity:       No  [x]
                                 Yes [_] Final Maturity Date: __________________

                                                 Optional              Optional
                          Redemption             Repayment             Repayment
Redeemable On              Price(s)               Date(s)              Price(s)
-------------             ----------             ---------             ---------
     N/A                     N/A                    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: N/A

[_]   Federal Funds Effective Rate

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

[_]   Treasury Rate                       Interest Reset Period: Daily

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

[_]   LIBOR Telerate

[_]   Prime Rate

[_]   CMT Rate

Initial Interest Rate: 4.50%              Interest Payment Period: Quarterly

Index Maturity: N/A

Spread (plus or minus): +0.14%

* Commencing June 6, 2006 and on the 6th of each September, December, March and
June thereafter, up to and including the maturity date.

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