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                                                                EXHIBIT 4.33

                   COMMON SECURITIES GUARANTEE AGREEMENT

          This COMMON SECURITIES GUARANTEE AGREEMENT (the "Common Securities
Guarantee"), dated as of May 19, 2000, is executed and delivered by GREATER BAY
BANCORP, a California corporation (the "Guarantor"), for the benefit of the
Holders (as defined herein) from time to time of the Common Securities (as
defined herein) of GBB CAPITAL IV, a Delaware business trust (the "Issuer").

          WHEREAS, pursuant to an Amended and Restated Declaration of Trust (the
"Declaration"), dated as of May 19, 2000, by and among the Trustees of the
Issuer named therein, the Guarantor, as sponsor, and the holders from time to
time of undivided beneficial interests in the assets of the Issuer, the Issuer
is issuing on the date hereof 1,268 common securities having an aggregate
liquidation amount of one million two hundred sixty-eight thousand dollars
($1,268,000), to meet the capital requirements of the Trust; such common
securities being designated the 10.75% Common Securities (the "Common
Securities").

          WHEREAS, as incentive for the Holders to purchase the Common
Securities, the Guarantor desires irrevocably and unconditionally to agree, to
the extent set forth in this Common Securities Guarantee, to pay the Guarantee
Payments (as defined herein) to the Holders of the Common Securities and to make
certain other payments on the terms and conditions set forth herein; and

          WHEREAS, the Guarantor is also executing and delivering the Series A
Capital Securities Guarantee Agreement, dated as of May 19, 2000 (the "Series A
Capital Securities Guarantee"), for the benefit of the holders of the Series A
Capital Securities (as defined in the Declaration) and upon consummation of the
Exchange Offer (as defined in the Declaration) will execute and deliver the
Series B Capital Securities Guarantee Agreement (the "Series B Capital
Securities Guarantee") for the benefit of the holders of the Series B Capital
Securities (as defined in the Declaration); it being understood that if an Event
of Default (as defined in the Declaration) has occurred and is continuing, the
rights of Holders of the Common Securities to receive Guarantee Payments under
this Common Securities Guarantee are subordinated, to the extent and in the
manner set forth herein, to the rights of holders of Capital Securities (as
defined in the Declaration) to receive Guarantee Payments under the Series A
Capital Securities Guarantee and the Series B Capital Securities Guarantee, as
the case may be.

          NOW, THEREFORE, in consideration of the purchase by each Holder of the
Common Securities, which purchase the Guarantor hereby acknowledges shall
benefit the Guarantor, the Guarantor executes and delivers this Common
Securities Guarantee for the benefit of the Holders.

                                   ARTICLE I
                        DEFINITIONS AND INTERPRETATION

SECTION 1.1 Definitions and Interpretation
            ------------------------------

            In this Common Securities Guarantee, unless the context otherwise
requires:

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          (a)  capitalized terms used in this Common Securities Guarantee but
not defined in the preamble above have the respective meanings assigned to them
in this Section 1.1;

          (b)  terms defined in the Declaration as at the date of execution of
this Common Securities Guarantee have the same meaning when used in this Common
Securities Guarantee unless otherwise defined in this Common Securities
Guarantee;

          (c)  a term defined anywhere in this Common Securities Guarantee has
the same meaning throughout;

          (d)  all references to "the Common Securities Guarantee" or "this
Common Securities Guarantee" are references to this Common Securities Guarantee
as modified, supplemented or amended from time to time;

          (e)  all references in this Common Securities Guarantee to Articles
and Sections are references to Articles and Sections of this Common Securities
Guarantee unless otherwise specified;

          (f)  a term defined in the Trust Indenture Act has the same meaning as
in the Trust Indenture Act unless otherwise defined in this Common Securities
Guarantee; and

          (g)  a reference to the singular includes the plural and vice versa.

          "Guarantee Payments" means the following payments or distributions,
without duplication, with respect to the Common Securities, to the extent not
paid or made by or on behalf of the Issuer: (i) any accumulated and unpaid
Distributions (as defined in the Declaration) that are required to be paid on
such Common Securities, to the extent the Issuer has funds legally available
therefor at such time, (ii) the redemption price, including all accumulated and
unpaid Distributions to the date of redemption (the "Redemption Price"), to the
extent the Issuer has funds legally available therefor at such time, with
respect to any Common Securities called for redemption, and (iii) upon a
voluntary or involuntary dissolution, winding-up or liquidation of the Issuer
(other than in connection with the distribution of Debentures (as defined in the
Declaration) to the Holders in exchange for Common Securities or in connection
with the redemption of the Common Securities, in each case as provided in the
Declaration), the lesser of (a) the aggregate of the liquidation amount and all
accumulated and unpaid Distributions on the Common Securities to the date of
payment, to the extent the Issuer has funds legally available therefor at such
time, and (b) the amount of assets of the Issuer remaining available for
distribution to the Holders after satisfaction of liabilities to creditors of
the Issuer as required by applicable law (in either case, the "Liquidation
Distribution"). If an Event of Default under the Declaration, the Series A
Capital Securities Guarantee Agreement or the Series B Capital Securities
Guarantee Agreement has occurred and is continuing, no Guarantee Payments with
respect to the Common Securities shall be made until holders of Capital
Securities shall be paid in full the Guarantee Payments to which they are
entitled under the Series A Capital Securities Guarantee and the Series B
Capital Securities Guarantee, as the case may be.

          "Holder" means any holder, as registered on the books and records of
the Issuer, of any Common Securities.

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          "Other Guarantees" means all guarantees, other than this Common
Securities Guarantee, to be issued by the Guarantor with respect to common
securities (if any) similar to the Common Securities issued by trusts other than
the Issuer to be established by the Guarantor (if any), in each case similar to
the Issuer.

                                  ARTICLE II
                                   GUARANTEE

SECTION 2.1    Guarantee
               ---------

               The Guarantor irrevocably and unconditionally agrees to pay in
full to the Holders the Guarantee Payments (without duplication of amounts
theretofore paid by the Issuer), as and when due, regardless of any defense,
right of set-off or counterclaim which the Issuer may have or assert. The
Guarantor fully, knowingly and unconditionally waives any right the Guarantor
may have to revoke this Guarantee under Section 2815 of the California Civil
Code or otherwise. The Guarantor's obligation to make a Guarantee Payment may be
satisfied by direct payment of the required amounts by the Guarantor to the
Holders or by causing the Issuer to pay such amounts to the Holders.

SECTION 2.2    Waiver of Notice and Demand
               ---------------------------

               The Guarantor hereby waives notice of acceptance of this Common
Securities Guarantee and of any liability to which it applies or may apply,
presentment, demand for payment, any right to require a proceeding first against
the Issuer or any other Person before proceeding against the Guarantor, protest,
notice of nonpayment, notice of dishonor, notice of redemption and all other
notices and demands.

SECTION 2.3    Obligations Not Affected
               ------------------------

               The obligations, covenants, agreements and duties of the
Guarantor under this Common Securities Guarantee shall in no way be affected or
impaired by reason of the happening from time to time of any of the following:

               (a)  the release or waiver, by operation of law or otherwise, of
the performance or observance by the Issuer of any express or implied agreement,
covenant, term or condition relating to the Common Securities to be performed or
observed by the Issuer;

               (b)  the extension of time for the payment by the Issuer of all
or any portion of the Distributions, Redemption Price, Liquidation Distribution
or any other sums payable under the terms of the Common Securities or the
extension of time for the performance of any other obligation under, arising out
of, or in connection with, the Common Securities;

               (c)  any failure, omission, delay or lack of diligence on the
part of the Holders to enforce, assert or exercise any right, privilege, power
or remedy conferred on the Holders pursuant to the terms of the Common
Securities, or any action on the part of the Issuer granting indulgence or
extension of any kind;

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               (d)  the voluntary or involuntary liquidation, dissolution, sale
of any collateral, receivership, insolvency, bankruptcy, assignment for the
benefit of creditors, reorganization, arrangement, composition or readjustment
of debt of, or other similar proceedings affecting, the Issuer or any of the
assets of the Issuer;

               (e)  any invalidity of, or defect or deficiency in, the Common
Securities;

               (f)  the settlement or compromise of any obligation guaranteed
hereby or hereby incurred; or

               (g)  any other circumstance whatsoever that might otherwise
constitute a legal or equitable discharge or defense of a guarantor;

it being the intent of this Section 2.3 that the obligations of the Guarantor
with respect to the Guarantee Payments shall be absolute and unconditional under
any and all circumstances.

               There shall be no obligation of the Holders to give notice to, or
obtain consent of, the Guarantor with respect to the happening of any of the
foregoing.

SECTION 2.4    Rights of Holders
               -----------------

               The Guarantor expressly acknowledges that any Holder of the
Common Securities may institute a legal proceeding directly against the
Guarantor to enforce its rights under this Common Securities Guarantee, without
first instituting a legal proceeding against the Issuer or any other Person.

SECTION 2.5    Guarantee of Payment
               --------------------

               This Common Securities Guarantee creates a guarantee of payment
and not of collection.

SECTION 2.6    Subrogation
               -----------

               The Guarantor shall be subrogated to all (if any) rights of the
Holders of the Common Securities against the Issuer in respect of any amounts
paid to such Holders by the Guarantor under this Common Securities Guarantee;
provided, however, that the Guarantor shall not (except to the extent required
--------  -------
by mandatory provisions of law) be entitled to enforce or exercise any rights
which it may acquire by way of subrogation or any indemnity, reimbursement or
other agreement, in all cases as a result of payment under this Common
Securities Guarantee, if, at the time of any such payment, any amounts are due
and unpaid under this Common Securities Guarantee. If any amount shall be paid
to the Guarantor in violation of the preceding sentence, the Guarantor agrees to
hold such amount in trust for the Holders and to pay over such amount to the
Holders.

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SECTION 2.7    Independent Obligations
               -----------------------

               The Guarantor acknowledges that its obligations hereunder are
independent of the obligations of the Issuer with respect to the Common
Securities and that the Guarantor shall be liable as principal and as debtor
hereunder to make Guarantee Payments pursuant to the terms of this Common
Securities Guarantee notwithstanding the occurrence of any event referred to in
subsections (a) through (g), inclusive, of Section 2.3 hereof.


                                  ARTICLE III
                   LIMITATION OF TRANSACTIONS; SUBORDINATION

SECTION 3.1    Limitation of Transactions
               --------------------------

               So long as any Common Securities remain outstanding, the
Guarantor will not (i) declare or pay any dividends or distribution on, or
redeem, purchase, acquire or make a liquidation payment with respect to any of
the Guarantor's capital stock, (ii) make any payment of principal of, or
interest or premium, if any, on or repay, repurchase or redeem any debt
securities of the Guarantor (including Other Debentures, as defined in the
Indenture) that rank pari passu with or junior in right of payment to the
Debentures or (iii) make any guarantee payments with respect to any guarantee by
the Guarantor of the debt securities of any subsidiary of the Guarantor
(including Other Guarantees, as defined in the Indenture) if such guarantee
ranks pari passu with or junior in right of payment to the Debentures (other
than (a) dividends or distributions in shares of, or options, warrants or rights
to subscribe for or purchase shares of, common stock of the Guarantor, (b) any
declaration of a dividend in connection with the implementation of a
shareholders' rights plan, or the issuance of stock under any such plan in the
future, or the redemption or repurchase of any such rights pursuant thereto, (c)
payments under the Series A Capital Securities Guarantee and the Series B
Capital Securities Guarantee, (d) as a result of a reclassification of the
Guarantor's capital stock or the exchange or the conversion of one class or
series of the Guarantor's capital stock for another class or series of the
Guarantor's capital stock, (e) the purchase of fractional interests in shares of
the Guarantor's capital stock pursuant to the conversion or exchange provisions
of such capital stock or the security being converted or exchanged, and (f)
purchases of common stock related to the issuance of common stock or rights
under any of the Guarantor's benefit or compensation plans for its directors,
officers or employees or any of the Guarantor's dividend reinvestment plans) if
at such time (1) there shall have occurred any event of which the Guarantor has
actual knowledge that (A) is, or with the giving of notice or the lapse of time,
or both, would be, an Event of Default and (B) in respect of which the Guarantor
shall not have taken reasonable steps to cure, (2) if such Debentures are held
by the Property Trustee, the Guarantor shall be in default with respect to its
payment of any obligations under the Series A Capital Securities Guarantee or
the Series B Capital Securities Guarantee or (3) the Guarantor shall have given
notice of its election of the exercise of its right to commence an Extended
Interest Payment Period as provided in the Indenture and shall not have
rescinded such notice, and such Extended Interest Payment Period, or an
extension thereof, shall have commenced and be continuing.

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SECTION 3.2    Ranking
               -------

               This Common Securities Guarantee will constitute an unsecured
obligation of the Guarantor and will rank (i) subordinate and junior in right of
payment to the Senior Indebtedness (as defined in the Indenture), to the same
extent and in the same manner that the Debentures are subordinated to the Senior
Indebtedness pursuant to the Indenture, it being understood that the terms of
Article XV of the Indenture shall apply to the obligations of the Guarantor
under this Common Securities Guarantee as if such Article XV were set forth
herein in full, (ii) pari passu with the most senior preferred or preference
stock now or hereafter issued by the Guarantor and with any Other Guarantee and,
except as set forth herein or therein, the Series A Capital Securities
Guarantee, the Series B Capital Securities Guarantee and any guarantee now or
hereafter entered into by the Guarantor in respect of any preferred or
preference stock of any Affiliate of the Guarantor and (iii) senior to the
Guarantor's common stock.

                                  ARTICLE IV
                                  TERMINATION

SECTION 4.1    Termination
               -----------

               This Common Securities Guarantee shall terminate and be of no
further force or effect upon (i) full payment of the Redemption Price of all
Common Securities, (ii) the dissolution, winding-up or liquidation of the
Issuer, immediately following the full payment of the amounts payable in
accordance with the Declaration, or (iii) the distribution of all of the
Debentures to the Holders of the Trust Securities (as defined in the
Declaration). Notwithstanding the foregoing, this Common Securities Guarantee
will continue to be effective or will be reinstated, as the case may be, if at
any time any Holder of the Common Securities must restore payment of any sums
paid under the Common Securities or under this Common Securities Guarantee.

                                   ARTICLE V
                                 MISCELLANEOUS

SECTION 5.1    Successors and Assigns
               ----------------------

               All guarantees and agreements contained in this Common Securities
Guarantee shall bind the successors, assigns, receivers, trustees and
representatives of the Guarantor and shall inure to the benefit of the Holders
of the Common Securities then outstanding.

SECTION 5.2    Amendments
               ----------

               Except with respect to any changes which do not adversely affect
in any material respect the rights of the Holders (in which case no consent of
the Holders will be required), this Common Securities Guarantee may only be
amended with the prior approval of the Holders of a majority in liquidation
amount of all the outstanding Common Securities. The provisions of Section 12.2
of the Declaration with respect to meetings of Holders of the Trust Securities
apply to the giving of such approval.

SECTION 5.3    Notices
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          All notices provided for in this Common Securities Guarantee shall be
in writing, duly signed by the party giving such notice, and shall be delivered,
telecopied or mailed by registered or certified mail, as follows:

          (a)  if given to the Issuer, in care of the Administrative Trustee at
the Issuer's mailing address set forth below (or such other address as the
Issuer may give notice of to the Holders of the Common Securities):

               GBB CAPITAL III
               c/o Greater Bay
               Bancorp
               2860 West Bayshore Road
               Palo Alto, California 94303
               Attention: Steven C. Smith
               Telephone:   (650) 813-8200
               Telecopier:  (650) 494-9193


          (b)  if given to the Guarantor, at the Guarantor's mailing address set
forth below (or such other address as the Guarantor may give notice of to the
Holders of the Common Securities):

               GREATER BAY BANCORP
               2860 West Bayshore Road
               Palo Alto, California 94303
               Attention: Steven C. Smith
               Telephone:   (650) 813-8200
               Telecopier:  (650) 494-9193


          (c)  if given to any Holder of the Common Securities, at the address
set forth on the books and records of the Issuer.

          All such notices shall be deemed to have been given when received in
person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid except that if a notice or other document is refused delivery or
cannot be delivered because of a changed address of which no notice was given,
such notice or other document shall be deemed to have been delivered on the date
of such refusal or inability to deliver.

SECTION 5.4    Benefit
               -------

          This Common Securities Guarantee is solely for the benefit of the
Holders of the Common Securities and is not separately transferrable from the
Common Securities.

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SECTION 5.5    Governing Law
               -------------

               THIS COMMON SECURITIES GUARANTEE SHALL BE GOVERNED BY, AND
CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK
WITHOUT REGARD TO CONFLICT OF LAW PRINCIPLES THEREOF.

               This Common Securities Guarantee is executed as of the day and
year first above written.

                              GREATER BAY BANCORP


                              By: /s/ Shawn E. Saunders
                                  ---------------------
                                  Name:  Shawn E. Saunders
                                  Title: Senior Vice President, Finance
                                         and Accounting

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