<PAGE>

                                                                 Exhibit 4(b)(2)


                 Form of Medium-Term Note, Series B (Fixed Rate)

UNLESS AND UNTIL IT IS EXCHANGED IN WHOLE OR IN PART FOR NOTES IN CERTIFICATED
FORM, THIS NOTE MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO A
NOMINEE OF THE DEPOSITARY OR BY A NOMINEE OF THE DEPOSITARY TO THE DEPOSITARY OR
ANOTHER NOMINEE OF THE DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A
SUCCESSOR DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITARY. UNLESS THIS
CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST
COMPANY (55 WATER STREET, NEW YORK, NEW YORK), TO THE ISSUER OR ITS AGENT FOR
REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE ISSUED IS
REGISTERED IN THE NAME OF CEDE & CO. OR SUCH OTHER NAME AS REQUESTED BY AN
AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY AND ANY PAYMENT IS
MADE TO CEDE & CO., ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL, SINCE THE REGISTERED OWNER HEREOF,
CEDE & CO., HAS AN INTEREST HEREIN.

REGISTERED                                    $

No. FX -                                           CUSIP #


                         THE BEAR STEARNS COMPANIES INC.

                           MEDIUM-TERM NOTE, SERIES B
                                  (FIXED RATE)


Interest Rate:

Interest Payment Dates:

Original Issue Date:                       Redeemable On and After:

Maturity Date:                             Optional Repayment Date(s):


<PAGE>


         THE BEAR STEARNS COMPANIES INC., a Delaware corporation (the
"Company"), for value received, hereby promises to pay to CEDE & CO., or
registered assigns, the principal amount stated above on the Maturity Date shown
above and to pay interest thereon at the rate per annum equal to the Interest
Rate shown above until the principal hereof is fully paid or duly made available
for payment. The Company will pay interest (computed on the basis of a 360-day
year of twelve 30-day months) in arrears on __________ of each year (each an
"Interest Payment Date") commencing with the Interest Payment Date next
following the Original Issue Date specified above (the "Original Issue Date")
provided that, if the Original Issue Date is later than the Regular Record Date
and prior to the next succeeding Interest Payment Date, interest shall be so
payable commencing with the second Interest Payment Date following the Original
Issue Date, and on the Maturity Date shown above, the date of redemption (the
"Redemption Date"), if any, or the date of optional repayment (the "Optional
Repayment Date"), if any, on said principal amount at the Interest Rate per
annum specified above. Interest on this Note will accrue from the most recent
Interest Payment Date to which interest has been paid or duly provided for or,
if no interest has been paid, from the Original Issue Date shown above until the
principal hereof has been paid or made available for payment. The interest so
payable, and punctually paid or duly provided for, on the Interest Payment Date
referred to above, will, as provided in the Indenture referred to below, be paid
to the Person in whose name this Note (or one or more Predecessor Securities) is
registered at the close of business on the Regular Record Date for such
interest, which shall be the date, whether or not a Business Day, 15 calendar
days immediately preceding such Interest Payment Date; PROVIDED,
HOWEVER, that interest payable on the Maturity Date shown above or, if
applicable, upon redemption or optional repayment, will be payable to the Person
to whom the principal hereof shall be payable; and PROVIDED, FURTHER, HOWEVER,
that if such Interest Payment Date would fall on a day that is not a Business
Day, such Interest Payment Date shall be the following day that is a Business
Day. Any such interest which is payable, but is not punctually paid or duly
provided for, on any Interest Payment Date shall forthwith cease to be payable
to the Holder on such Regular Record Date, and may be paid to the Person in
whose name this Note (or one or more Predecessor Securities) is registered at
the close of business on a Special Record Date for the payment of such Defaulted
Interest to be fixed by the Trustee, notice whereof shall be given to the Holder
of this Note not less than ten days prior to such Special Record Date, or may be
paid at any time in any other lawful manner not inconsistent with the
requirements of any securities exchange on which the Notes may be listed and
upon such notice as may be required by such exchange, all as more fully provided
in the Indenture.

         Payment of the principal of and interest on this Note shall be made at
the office or agency of the Trustee maintained for that purpose in the Borough
of Manhattan, The City of New York, in such coin or currency of the United
States of America as at the time of payment is legal tender for the payment of
public and private debt; PROVIDED, HOWEVER, that payment of interest on any
Interest Payment Date (other than the Maturity Date or Redemption Date or
Optional Repayment Date, if any) may be made at the option of the Company by
check mailed to the address of the Person entitled thereto as such address shall
appear in the Security Register, or by wire transfer of immediately available
funds, if the registered holder of at least $10,000,000 in principal amount of
Notes entitled to such interest has so requested by a notice in writing
delivered to the Trustee not less than 16 days prior to the Interest Payment
Date on which such payment is due, which notice shall provide appropriate
instructions for such transfer.

         The principal hereof and interest due at maturity will be paid upon
maturity in immediately available funds against presentation of this Note at the
office or agency of the Trustee maintained for that purpose in the Borough of
Manhattan, The City of New York.

         REFERENCE IS HEREBY MADE TO THE FURTHER PROVISIONS OF THIS NOTE SET
FORTH ON THE REVERSE HEREOF, WHICH FURTHER PROVISIONS SHALL FOR ALL PURPOSES
HAVE THE SAME EFFECT AS IF SET FORTH ON THE FACE HEREOF.

         This Note shall be governed by and construed in accordance with the
laws of the State of New York.

         This Note is one of the series of Medium-Term Notes, Series B, of the
Company.

<PAGE>

         Unless the certificate of authentication hereon has been executed by
The Chase Manhattan Bank, the Trustee under the Indenture, or its successor
thereunder by the manual signature of one of its authorized signatories, this
Note shall not be entitled to any benefit under the Indenture or be valid or
obligatory for any purpose.


<PAGE>



         IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed under its corporate seal.

Dated:

                                          THE BEAR STEARNS COMPANIES INC.

                                          By: __________________________________



ATTEST:


_________________________________
Secretary

[Corporate Seal]

                          CERTIFICATE OF AUTHENTICATION

         This is one of the Securities of the series designated therein referred
to in the within-mentioned Indenture.

                                          THE CHASE MANHATTAN BANK, as Trustee

                                             By:_____________________________
                                                Authorized Signature


<PAGE>



                                [REVERSE OF NOTE]

                         THE BEAR STEARNS COMPANIES INC.

                           MEDIUM-TERM NOTE, SERIES B
                                  (FIXED RATE)

         This Note is one of a duly authorized issue of debentures, notes or
other evidences of indebtedness (hereinafter called the "Securities") of the
Company of the series hereinafter specified, all such Securities issued and to
be issued under the Indenture dated as of May 31, 1991, as amended (herein
called the "Indenture") between the Company and The Chase Manhattan Bank, as
Trustee (herein called the "Trustee," which term includes any successor trustee
under the Indenture), to which Indenture and all indentures supplemental thereto
reference is hereby made for a statement of the respective rights and
limitations of rights thereunder of the Company, the Trustee and the Holders of
the Securities, and the terms upon which the Securities are, and are to be,
authenticated and delivered. As provided in the Indenture, Securities may be
issued in one or more series, which different series may be issued in various
aggregate principal amounts, may mature at different times, may bear interest,
if any, at different rates, may be subject to different redemption provisions,
if any, may be subject to different repayment provisions, if any, may be subject
to different sinking, purchase or analogous funds, if any, may be subject to
different covenants and Events of Default and may otherwise vary as in the
Indenture provided or permitted. This Note is one of the series of the
Securities designated as Medium-Term Notes, Series B (the "Notes"). The Notes of
this series may be issued at various times with different maturity dates,
redemption dates and different principal repayment provisions, may bear interest
at different rates and may otherwise vary, all as provided in the Indenture.

         If so specified on the face of this Note, this Note may be redeemed by
the Company on and after the date so indicated on the face hereof. If no such
date is set forth on the face hereof, this Note may not be redeemed prior to
maturity. On and after such date, if any, from which this Note may be redeemed,
this Note may be redeemed in whole or in part in increments of $1,000 (provided
that any remaining principal amount of this Note shall be at least $25,000), at
the option of the Company, at a redemption price equal to 100% of the principal
amount to be redeemed, together with interest thereon payable to the Redemption
Date, on notice given not more than 60 nor less than 30 days prior to the
Redemption Date. If less than all the Outstanding Notes having such terms as
specified by the Company are to be redeemed, the particular Notes to be redeemed
shall be selected by the Trustee not more than 60 days prior to the Redemption
Date from the Outstanding Notes having such terms as specified by the Company
not previously called for redemption, by such method as the Trustee shall deem
fair and appropriate. The notice of such redemption shall specify which Notes
are to be redeemed. In the event of redemption of this Note, in part only, a new
Note or Notes in authorized denominations for the unredeemed portion hereof
shall be issued in the name of the Holder hereof upon the surrender hereof.

         If so specified on the face of this Note, this Note will be subject to
repayment at the option of the Holder hereof on the Optional Repayment Date(s).
If no Optional Repayment Date is set forth on the face hereof, this Note may not
be repaid at the option of the Holder prior to maturity. On and after the
Optional Repayment Date, if any, from which this Note may be repaid at the
option of the Holder, this Note shall be repayable in whole or in part in
increments of $1,000 (provided that any remaining principal amount of this Note
shall be at least $25,000) at a repayment price equal to 100% of the principal
amount to be repaid, together with interest thereon payable to the Optional
Repayment Date. For this Note to be repaid in whole or in part at the option of
the Holder hereof, the Trustee must receive not less than 30 nor more than 60
days prior to the Optional Repayment Date (i) this Note with the form entitled
"Option to Elect Repayment," which appears below, duly completed or (ii) a
telegram, telex, facsimile transmission or a letter from a member of a national
securities exchange or the National Association of Securities Dealers, Inc. or a
commercial bank or trust company in the United States of America setting forth
the name of the Holder of this Note, the principal amount of this Note, the
certificate number of this Note or a description of this Note's tenor or terms,
the principal amount of this Note to be repaid, a statement that the option to
elect repayment is being exercised thereby and a guarantee that this Note with
the form entitled "Option to Elect Repayment," which appears below, duly
completed, will be received by the Trustee no later than five Business Days
after the date of such telegram, telex, facsimile transmission or letter and
this Note


<PAGE>

and such form duly completed are received by the Trustee by such fifth Business
Day. Exercise of the repayment option shall be irrevocable.

         If any Event of Default with respect to the Notes shall occur and be
continuing, the Trustee or the Holders of not less than 25% in principal amount
of the Outstanding Notes may declare the principal of all the Notes due and
payable in the manner and with the effect provided in the Indenture.

         The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Securities of each series to be
affected under the Indenture at any time by the Company and the Trustee with the
consent of the Holders of 66-2/3% in aggregate principal amount of the
Securities at the time Outstanding of each series affected thereby. The
Indenture also contains provisions permitting the Holders of specified
percentages in aggregate principal amount of the Securities of each series at
the time Outstanding, on behalf of the Holders of all Securities of each series,
to waive compliance by the Company with certain provisions of the Indenture and
certain past defaults under the Indenture and their consequences. Any such
consent or waiver by the Holder of this Note shall be conclusive and binding
upon such Holder and upon future Holders of this Note and of any Note issued
upon the registration of transfer hereof or in exchange hereof or in lieu hereof
whether or not notation of such consent or waiver is made upon this Note.

         Holders of Securities may not enforce their rights pursuant to the
Indenture or the Securities except as provided in the Indenture. No reference
herein to the Indenture and no provision of this Note or the Indenture shall
alter or impair the obligation of the Company, which is absolute and
unconditional, to pay the principal of and interest on this Note at the time,
place, and rate, and in the coin or currency, herein prescribed.

         As provided in the Indenture and subject to certain limitations therein
set forth, the transfer of this Note may be registered on the Security Register
of the Company, upon surrender of this Note for registration of transfer at the
office or agency of the Company in the Borough of Manhattan, The City of New
York, duly endorsed by, or accompanied by a written instrument of transfer in
form satisfactory to the Company, and this Note duly executed by, the Holder
hereof or by his attorney duly authorized in writing and thereupon one or more
new Notes, of authorized denominations and for the same aggregate principal
amount, will be issued to the designated transferee or transferees.

         The Notes are issuable only in registered form without coupons in
denominations of $25,000 or any amount in excess thereof which is an integral
multiple of $1,000. As provided in the Indenture and subject to certain
limitations therein set forth, this Note is exchangeable for a like aggregate
principal amount of Notes of different authorized denomination as requested by
the Holder surrendering the same.

         No service charge will be made for any such registration of transfer or
exchange, but the Company may require payment of a sum sufficient to cover any
tax or other governmental charge payable in connection therewith.

         Prior to the due presentment of this Note for registration of transfer,
the Company, the Trustee and any agent of the Company or the Trustee may treat
the Person in whose name this Note is registered as the owner hereof for all
purposes, whether or not this Note be overdue, and neither the Company, the
Trustee nor any such agent shall be affected by notice of the contrary.

         The interest rate payable with respect to this Note shall in no event
be higher than the maximum rate, if any, permitted by applicable law.

         All capitalized terms used in this Note and not otherwise defined
herein shall have the meanings assigned to them in the Indenture.


<PAGE>

                      ------------------------------------


                                  ABBREVIATIONS

The following abbreviations, when used in the inscription on the face of this
instrument, shall be construed as though they were written out in full according
to applicable laws or regulations:

TEN COM        -       as tenants in common

TEN ENT        -       as tenants by the entireties

JT TEN         -       as joint tenants with right of survivorship and not as
                       tenants in common

UNIF GIFT MIN ACT -          ___________________ Custodian ___________________
                             (Cust)                              (Minor)
                             Under Uniform Gifts to Minors Act

                             ____________________________________________(State)


Additional abbreviations may also be used though not in the above list.

                      ------------------------------------


                            OPTION TO ELECT REPAYMENT

         The undersigned hereby irrevocably request(s) and instruct(s) the
Company to repay this Note (or portion thereof specified below) pursuant to its
terms on ____________, 19___ (the "Optional Repayment Date") at a price equal to
the principal amount thereof, together with interest to the Optional Repayment
Date, to the undersigned at

--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
        (Please print or typewrite name and address of the undersigned.)

         For this Note to be repaid the Trustee must receive at 450 West 33rd
Street, New York, New York 10001, Attention: Debt Operations -- 8th Floor, or at
such other place or places of which the Company shall from time to time notify
the Holder of this Note, not more than 60 days nor less than 30 days prior to
the Optional Repayment Date, this Note with this "Option to Elect Repayment"
form duly completed.


<PAGE>

         If less than the entire principal amount of this Note is to be repaid,
specify the portion thereof (which shall be increments of $1,000) which the
Holder elects to have repaid: $_________________; and specify the denomination
or denominations (which shall be $25,000 or an integral multiple of $1,000 in
excess of $25,000) of the Notes to be issued to the Holder for the portion of
this Note that will be issued for the portion not being repaid):

Date:_________________                          ________________________________
                                                Note: The signature to this
                                                Option to Elect Repayment must
                                                correspond with the same as
                                                written upon the face of this
                                                Note in every particular without
                                                alteration or enlargement.

                      ------------------------------------


                                   ASSIGNMENT

                       FOR VALUE RECEIVED, the undersigned
                 hereby sell(s), assign(s) and transfer(s) unto

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PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE

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PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS INCLUDING POSTAL ZIP CODE OF ASSIGNEE

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the within Note and all rights thereunder, hereby irrevocably constituting and
appointing


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Attorney to transfer said Note on the books of the Company, with full power of
substitution in the premises.

Dated:
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------------------------------------
         (Signature Guarantee)