PRICING SUPPLEMENT NO. 45                                         Rule 424(b)(3)
DATED:   January 4, 2005                                     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: $50,000,000   Floating Rate Notes [ ]   Book Entry Notes [x]

Original Issue Date: 1/7/2005   Fixed Rate Notes [x]      Certificated Notes [ ]

Maturity Date: 1/7/2010         CUSIP#: 073928J38

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: 4.245%

Interest Payment Date(s): *

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

Interest Rate Basis:                    Maximum Interest Rate:

[ ]  Commercial Paper Rate              Minimum Interest Rate:

[ ]  Federal Funds Effective Rate

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

[ ]  Treasury Rate                      Interest Reset Period:

[ ]  LIBOR Reuters                      Interest Payment Date(s):

[ ]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate:                   Interest Payment Period:

Index Maturity:

Spread (plus or minus):

* On the 7th of each July and January, including the maturity date.

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