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                                                                     Exhibit 4.1

                                  Exhibit 4.1

                         SECURITIES PURCHASE AGREEMENT

     This SECURITIES PURCHASE AGREEMENT (this "Agreement"), dated as of March
                                               ---------
22, 2000 is made by and among Greater Bay Bancorp, a California corporation,
with headquarters located at 2860 West Bayshore Road, Palo Alto, California (the
"Company"), and the investors named on the signature pages hereto (the
 -------
"Investors").
----------

                                   RECITALS:

     A.  The Company and the Investors are executing and delivering this
Agreement in reliance upon the exemption from securities registration afforded
by Section 4(2) of the Securities Act and Rule 506 under Regulation D.

     B.  The Investors desire, upon the terms and conditions stated in this
Agreement, to purchase shares of the Company's Common Stock, for an aggregate
purchase price of $12,000,000.  The purchase price per share of the Common Stock
is $37.00.

     C.  Contemporaneously with the execution and delivery of this Agreement,
the parties hereto are executing and delivering a Registration Rights Agreement
under which the Company has agreed to provide certain registration rights under
the Securities Act, the rules and regulations promulgated thereunder and
applicable state securities laws.

     D.  The capitalized terms used herein and not otherwise defined have the
meanings given them in Article 8 hereof.

     In consideration of the premises and the mutual covenants contained herein
and other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the Company and the Investors hereby agree as follows:

                                   ARTICLE I
                        PURCHASE AND SALE OF SECURITIES

     1.1  Purchase and Sale of Securities.  At the Closing, subject to the terms
          -------------------------------
of this Agreement and the satisfaction or waiver of the conditions set forth in
Articles VI and VII hereof, the Company will issue and sell to each Investor,
and each Investor will (on a several and not a joint basis) purchase from the
Company, the number of shares of Common Stock set forth beneath such Investor's
name on the signature pages hereof.

     1.2  Payment.  Each Investor will pay the purchase price for the number of
          -------
Securities set forth beneath its name on the signature pages hereof, by wire
transfer of immediately available funds in accordance with the Company's written
wire instructions, upon delivery by the Company to each Investor of certificates
representing the Securities so purchased by such Investor and the Company will
deliver such certificates against delivery of the purchase price as described
above.
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     1.3  Closing Date.  Subject to the satisfaction or waiver of the conditions
          ------------
set forth in Articles VI and VII hereof, the Closing will take place at 12:00
p.m. Pacific Standard Time on March 23, 2000 or at another date or time agreed
upon by the parties to this Agreement (the "Closing Date"). The Closing will be
                                            ------- ----
held at the offices of Greater Bay Bancorp, 2860 West Bayshore Road, Palo Alto,
California, or at such other place as the parties agree.

                                  ARTICLE II
                   INVESTOR'S REPRESENTATIONS AND WARRANTIES

     Each Investor represents and warrants to the Company, severally and solely
with respect to itself and its purchase hereunder and not with respect to any
other Investor, that:

     2.1  Investment Purpose.  The Investor is purchasing the Securities for its
          ------------------
own account and not with a present view toward the public sale or distribution
thereof, except pursuant to sales registered or exempted from registration under
the Securities Act; provided, however, that by making the representation herein,
the Investor does not agree to hold any of the Securities for any minimum or
other specific term and reserves the right to dispose of the Securities at any
time in accordance with or pursuant to a registration statement or an exemption
under the Securities Act.

     2.2  Accredited Investor Status.  The Investor is an "accredited investor"
          --------------------------
as defined in Rule 501(a) of Regulation D.

     2.3  Reliance on Exemptions.  The Investor understands that the Securities
          ----------------------
are being offered and sold to it in reliance upon specific exemptions from the
registration requirements of United States federal and state securities laws and
that the Company is relying upon the truth and accuracy of, and the Investor's
compliance with, the representations, warranties, agreements, acknowledgments
and understandings of the Investor set forth herein in order to determine the
availability of such exemptions and the eligibility of the Investor to acquire
the Securities.

     2.4  Information.  The Investor and its advisors, if any, have been
          -----------
furnished with all materials relating to the business, finances and operations
of the Company, and materials relating to the offer and sale of the Securities,
that have been requested by the Investor or its advisors, if any. The Investor
and its advisors, if any, have been afforded the opportunity to ask questions of
the Company. Neither such inquiries nor any other due diligence investigation
conducted by the Investor or any of its advisors or representatives modify,
amend or affect the Investor's right to rely on the Company's representations
and warranties contained in Article III below. The Investor acknowledges and
understands that its investment in the Securities involves a significant degree
of risk, including the risks reflected in the SEC Documents.

     2.5  Governmental Review.  The Investor understands that no United States
          -------------------
federal or state agency or any other government or governmental agency has
passed upon or made any recommendation or endorsement of the Securities or an
investment therein.

     2.6  Transfer or Resale.  The Investor understands that:
          ------------------

          (a)  except as provided in the Registration Rights Agreement, the
Securities have not been and are not being registered under the Securities Act
or any applicable state securities laws and, consequently, the Investor may have
to bear the risk of owning the Securities

                                       2
<PAGE>

for an indefinite period of time because the Securities may not be transferred
unless (i) the resale of the Securities is registered pursuant to an effective
registration statement under the Securities Act; (ii) the Investor has delivered
to the Company an opinion of counsel (in form, substance and scope customary for
opinions of counsel in comparable transactions) to the effect that the
Securities to be sold or transferred may be sold or transferred pursuant to an
exemption from such registration; (iii) the Securities are sold or transferred
pursuant to Rule 144; or (iv) the Securities are sold or transferred to an
affiliate (as defined in Rule 144) of the Investor pursuant to an exemption
from registration under the Securities Act.

          (b)  any sale of the Securities made in reliance on Rule 144 may be
made only in accordance with the terms of Rule 144 and, if Rule 144 is not
applicable, any resale of the Securities under circumstances in which the seller
(or the person through whom the sale is made) may be deemed to be an underwriter
(as that term is defined in the Securities Act) may require compliance with some
other exemption under the Securities Act or the rules and regulations of the SEC
thereunder; and

          (c)  except as set forth in the Registration Rights Agreement, neither
the Company nor any other person is under any obligation to register the
Securities under the Securities Act or any state securities laws or to comply
with the terms and conditions of any exemption thereunder.

     2.7  Legends.  The Investor understands that until (a) the Securities may
          -------
be sold by the Investor under Rule 144(k) or (b) such time as the resale of the
Securities have been registered under the Securities Act as contemplated by the
Registration Rights Agreement, the certificates representing the Securities will
bear a restrictive legend in substantially the following form (and a stop-
transfer order may be placed against transfer of the certificates for such
Securities):

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
     UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY
     STATE OF THE UNITED STATES.  THE SECURITIES MAY NOT BE SOLD, TRANSFERRED OR
     ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT FOR THE
     SECURITIES UNDER APPLICABLE SECURITIES LAWS, OR UNLESS OFFERED, SOLD OR
     TRANSFERRED PURSUANT TO AN AVAILABLE EXEMPTION FROM THE REGISTRATION
     REQUIREMENTS OF THOSE LAWS.

     The legend set forth above will be removed and the Company will issue a
certificate without the legend to the holder of any certificate upon which it is
stamped, in accordance with the terms of Article V hereof.

     2.8  Authorization; Enforcement.  This Agreement and the Registration
          --------------------------
Rights Agreement have been duly and validly authorized, executed and delivered
on behalf of the Investor and are valid and binding agreements of the Investor
enforceable in accordance with their terms, subject to the effect of any
applicable bankruptcy, insolvency, reorganization, moratorium or similar laws
affecting the rights of creditors generally and the application of general
principles of equity.

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     2.9  Residency.  The Investor is a resident of the jurisdiction set forth
          ---------
immediately below such Investor's name on the signature pages hereto.

     2.10  Acknowledgements Regarding Placement Agent.  Purchaser acknowledges
           ------------------------------------------
that Keefe, Bruyette & Woods, Inc. is acting as placement agent (the "Placement
Agent") for the Securities being offered hereby and will be compensated by the
Company for acting in such capacity. Purchaser further acknowledges that the
Placement Agent has acted solely as placement agent in connection with the
offering of the Securities by the Company, that the information and data
provided to Purchaser in connection with the transactions contemplated hereby
have not been subjected to independent verification by the Placement Agent, and
that the Placement Agent makes no representation or warranty with respect to the
accuracy or completeness of such information, data or other related disclosure
material. Purchaser further acknowledges that in making its decision to enter
into this Agreement and purchase the Securities it has relied on its own
examination of the Company and the terms of, and consequences of, holding the
Securities. Purchaser further acknowledges that the provisions of this Section
2.10 are for the benefit of, and may be enforced by, the Placement Agent.

                                  ARTICLE III
                 REPRESENTATIONS AND WARRANTIES OF THE COMPANY

     The Company represents and warrants to the Investors that:

     3.1  Organization and Qualification.  The Company and each of the Banks is
          ------------------------------
duly incorporated, validly existing and in good standing under the laws of the
jurisdiction in which it is incorporated, with full power and authority
(corporate and other) to own, lease, use and operate its properties and to carry
on its business as and where now owned, leased, used, operated and conducted.
The Company and each of the Banks is duly qualified to do business and is in
good standing in every jurisdiction in which the nature of the business
conducted by it makes such qualification necessary, except where the failure to
be so qualified or in good standing would not have a Material Adverse Effect.

     3.2  Authorization; Enforcement.  (a) The Company has all requisite
          --------------------------
corporate power and authority to enter into and to perform its obligations under
this Agreement and the Registration Rights Agreement, to consummate the
transactions contemplated hereby and thereby and to issue the Securities in
accordance with the terms hereof and thereof; (b) the execution, delivery and
performance of this Agreement and the Registration Rights Agreement by the
Company and the consummation by it of the transactions contemplated hereby and
thereby (including without limitation the issuance of the Securities) have been
duly authorized by the Company's Board of Directors and no further consent or
authorization of the Company, its Board of Directors, or its shareholders is
required; (c) this Agreement and the Registration Rights Agreement have been
duly executed by the Company; and (d) each of this Agreement and the
Registration Rights Agreement constitutes a legal, valid and binding obligation
of the Company enforceable against the Company in accordance with its terms,
subject to the effect of any applicable bankruptcy, insolvency, reorganization,
or moratorium or similar laws affecting the rights of creditors generally and
the application of general principles of equity.

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<PAGE>

     3.3  Capitalization.  As of March 15, 2000, the authorized capital stock of
          --------------
the Company consists of (a) 24,000,000 shares of Common Stock, of which
14,376,768 shares are issued and outstanding as of March 20, 2000 and (b)
4,000,000 shares of preferred stock, no par value per share, of which 1,200,000
shares are designated as Series A Preferred Stock and none are issued and
outstanding. All of the outstanding shares of capital stock are duly authorized,
validly issued, fully paid and nonassessable. No shares of capital stock of the
Company, including the Securities issuable pursuant to this Agreement, are
subject to preemptive rights or any other similar rights of the shareholders of
the Company or any liens or encumbrances imposed through the actions or failure
to act of the Company. Except as disclosed in Schedule 3.3 and except for the
                                              ------------
transactions contemplated hereby, (i) there are no outstanding options,
warrants, scrip, rights to subscribe for, puts, calls, rights of first refusal,
agreements, understandings, claims or other commitments or rights of any
character whatsoever relating to, or securities or rights convertible into,
exercisable for, or exchangeable for any shares of capital stock of the Company,
or arrangements by which the Company is or may become bound to issue additional
shares of capital stock of the Company; (ii) there are no agreements or
arrangements (other than the Registration Rights Agreement) under which the
Company is obligated to register the sale of any of its securities under the
Securities Act and (iii) there are no anti-dilution or price adjustment
provisions contained in any security issued by the Company (or in any agreement
providing rights to security holders) that will be triggered by the issuance of
the Securities.  The Company has made available to the Investors if requested
true and correct copies of the Company's Articles of Incorporation, as amended,
as in effect on the date hereof, the Company's By-laws as in effect on the date
hereof and the terms of all securities convertible into or exercisable for
Common Stock of the Company and the material rights of the holders thereof in
respect thereto.

     3.4  Issuance of Securities.  The Securities are duly authorized and, upon
          ----------------------
issuance in accordance with the terms of this Agreement, will be validly issued,
fully paid and non-assessable, free from all taxes, liens, claims, encumbrances
and charges with respect to the issue thereof, will not be subject to preemptive
rights or other similar rights of shareholders of the Company, and will not
impose personal liability on the holders thereof.

     3.5  No Conflicts; No Violation.
          --------------------------

          (a)  The execution, delivery and performance of this Agreement and the
Registration Rights Agreement by the Company and the consummation by the Company
of the transactions contemplated hereby and thereby (including, without
limitation, the issuance of the Securities) will not (i) conflict with or result
in a violation of any provision of its Articles of Incorporation, as amended or
By-laws, as amended or (ii) violate or conflict with, or result in a breach of
any provision of, or constitute a default (or an event which with notice or
lapse of time or both could become a default) under, or give to others any
rights of termination, amendment (including without limitation, the triggering
of any anti-dilution provision), acceleration or cancellation of, any agreement,
indenture, patent, patent license, or instrument to which the Company or any of
the Banks is a party, or (iii) result in a violation of any law, rule,
regulation, order, judgment or decree (including U.S. federal and state
securities laws and regulations and regulations of any self-regulatory
organizations to which the Company or its securities are subject) applicable to
the Company or any of the Banks or by which any property or asset of the Company
or any of the Banks is bound or affected (except for such conflicts, breaches,
defaults,

                                       5
<PAGE>

terminations, amendments, accelerations, cancellations and violations as would
not, individually or in the aggregate, have a Material Adverse Effect).

          (b)  The Company is not in violation of its Articles of Incorporation,
as amended, or By-laws, as amended, and neither the Company nor the Banks is in
default (and no event has occurred which with notice or lapse of time or both
could put the Company or any of the Banks in default) under any agreement,
indenture or instrument to which the Company or any of the Banks is a party or
by which any property or assets of the Company or any of the Banks is bound or
affected, except for possible defaults as would not, individually or in the
aggregate, have a Material Adverse Effect.

          (c)  Neither the Company nor any of the Banks is conducting its
business in violation of any law, ordinance or regulation of any governmental
entity, the failure to comply with which would, individually or in the
aggregate, have a Material Adverse Effect.

          (d)  Except as specifically contemplated by this Agreement and as
required under the Securities Act and any applicable state securities laws or
any listing agreement with any securities exchange or automated quotation
system, the Company is not required to obtain any consent, authorization or
order of, or make any filing or registration with, any court or governmental
agency or any regulatory or self-regulatory agency in order for it to execute,
deliver or perform any of its obligations under this Agreement or the
Registration Rights Agreement, in each case in accordance with the terms hereof
or thereof, or to issue and sell the Securities in accordance with the terms
hereof. Except as set forth in Schedule 3.5, all consents, authorizations,
                               ------------
orders, filings and registrations which the Company is required to obtain
pursuant to the preceding sentence have been obtained or effected on or prior to
the date hereof. The Company is not in violation of the listing requirements of
Nasdaq.

     3.6  SEC Documents, Financial Statements.  Since December 31, 1997, the
          -----------------------------------
Company has timely filed all reports, schedules, forms, statements and other
documents required to be filed by it with the SEC pursuant to the reporting
requirements of the Exchange Act (all of the foregoing filed prior to the date
hereof and all exhibits included therein and financial statements and schedules
thereto and documents (other than exhibits) incorporated by reference therein,
being hereinafter referred to herein as the "SEC Documents"). The Company has
                                             -------------
delivered to each Investor, or each Investor has had access to, true and
complete copies of the SEC Documents, except for such exhibits and incorporated
documents.  As of their respective dates, the SEC Documents complied in all
material respects with the requirements of the Exchange Act or the Securities
Act, as the case may be, and the rules and regulations of the SEC promulgated
thereunder applicable to the SEC Documents, and none of the SEC Documents, at
the time they were filed with the SEC, contained any untrue statement of a
material fact or omitted to state a material fact required to be stated therein
or necessary in order to make the statements therein, in light of the
circumstances under which they were made, not misleading.  As of their
respective dates, the consolidated financial statements of the Company included
in the SEC Documents complied as to form in all material respects with
applicable accounting requirements and the published rules and regulations of
the SEC with respect thereto.  Such financial statements have been prepared in
accordance with U.S. generally accepted accounting principles, consistently
applied, during the periods involved (except (i) as may be otherwise indicated
in such financial statements or the notes thereto, or (ii) in the case of
unaudited interim consolidated statements, to

                                       6
<PAGE>

the extent they may not include footnotes or may be condensed or summary
statements) and fairly present in all material respects the consolidated
financial position of the Company as of the dates thereof and the consolidated
results of its operations and cash flows for the periods then ended (subject, in
the case of unaudited statements, to normal year-end audit adjustments). Except
as set forth in the financial statements included in the SEC Documents, the
Company has no liabilities, contingent or otherwise, other than (x) liabilities
incurred in the ordinary course of business subsequent to date of such financial
statements, (y) liabilities of the type not required under generally accepted
accounting principles to be reflected in such financial statements, and (z)
obligations under contracts and commitments not required under generally
accepted accounting principles to be reflected in such financial statements.
Such liabilities and obligations, would not, individually or in the aggregate,
have a Material Adverse Effect.

     3.7  Absence of Certain Changes.  Since December 31, 1999, there has been
          --------------------------
no material adverse change in the assets, liabilities, business, properties,
operations, financial condition, prospects or results of operations of the
Company on a consolidated basis.

     3.8  Absence of Litigation.  There is no action, suit, claim, proceeding,
          ---------------------
inquiry or investigation before or by any court, public board, government
agency, self-regulatory organization or body pending or, to the knowledge of the
Company, threatened against or affecting the Company or the Banks or any of
their officers or directors acting as such that would, individually or in the
aggregate, have a Material Adverse Effect.

     3.9  Intellectual Property Rights.  The Company and each of the Banks owns
          ----------------------------
or possesses the licenses or rights to use all patents, patent applications,
patent rights, inventions, know-how, trade secrets, trademarks, trademark
applications, service marks, service names, trade names and copyrights necessary
to enable it to conduct its business as now operated (the "Intellectual
                                                           ------------
Property"). There is no claim or action or proceeding pending or, to the
--------
Company's knowledge, threatened that challenges the right of the Company or any
of the Banks with respect to any Intellectual Property.

     3.10  Tax Status.  The Company has made or filed all federal, state and
           ----------
foreign income and all other tax returns, reports and declarations required by
any jurisdiction to which it is subject (unless and only to the extent that the
Company has set aside on its books provisions reasonably adequate for the
payment of all unpaid and unreported taxes) and has paid all taxes and other
governmental assessments and charges that are material in amount, shown or
determined to be due on such returns, reports and declarations, except those
being contested in good faith, and has set aside on its books provisions
reasonably adequate for the payment of all taxes for periods subsequent to the
periods to which such returns, reports or declarations apply. To the knowledge
of the Company, there are no unpaid taxes in any material amount claimed to be
due by the taxing authority of any jurisdiction, and the officers of the Company
know of no basis for any such claim. The Company has not executed a waiver with
respect to the statute of limitations relating to the assessment or collection
of any foreign, federal, state or local tax. None of the Company's tax returns
is presently being audited by any taxing authority.

     3.11  No Integrated Offering.  Neither the Company, nor any of its
           ----------------------
affiliates, nor any person acting on its or their behalf, has directly or
indirectly made any offers or sales in any security or solicited any offers to
buy any security under circumstances that would require

                                       7
<PAGE>

registration under the Securities Act of the issuance of the Securities to the
Investors. The issuance of the Securities to the Investors will not be
integrated with any other issuance of the Company's securities (past, current or
future) for purposes of the Securities Act or any applicable rules of Nasdaq.

     3.12  No Brokers.  The Company has taken no action which would give rise to
           ----------
any claim by any person for brokerage commissions, finder's fees or similar
payments relating to this Agreement or the transactions contemplated hereby,
except for dealings with Keefe, Bruyette & Woods, Inc., whose commissions and
fees will be paid for by the Company.

     3.13  Insurance.  The Company and each of the Banks is insured by insurers
           ---------
of recognized financial responsibility against such losses and risks and in such
amounts as management of the Company believes to be prudent and customary in the
businesses in which the Company and the Banks are engaged.

     3.14  Investment Company Status.  The Company is not and upon consummation
           -------------------------
of the sale of the Securities will not be an "investment company," a company
controlled by an "investment company" or an "affiliated person" of, or
"promoter" or "principal underwriter" for, an "investment company" as such terms
are defined in the Investment Company Act of 1940, as amended.

                                  ARTICLE IV
                                   COVENANTS

     4.1  Best Efforts.  Each party will use its commercially reasonable efforts
          ------------
to satisfy in a timely fashion each of the conditions to be satisfied by it
under Articles VI and VII of this Agreement.

     4.2  Form D; Blue Sky Laws.  The Company will file a Notice of Sale of
          ---------------------
Securities on Form D with respect to the Securities, as required under
Regulation D, and to provide a copy thereof to each Investor promptly after such
filing.  The Company will, on or before the Closing Date, take such action as it
reasonably determines to be necessary to qualify the Securities for sale to the
Investors under this Agreement under applicable securities (or "blue sky") laws
of the states of the United States (or to obtain an exemption from such
qualification), and will provide evidence of any such action so taken to the
Investors on or prior to the date of the Closing.

     4.3  Reporting Status; Eligibility to Use Form S-3.  The Company's Common
          ----------------------------------------------
Stock is registered under Section 12 of the Exchange Act. The Company will file
with the SEC a Current Report on Form 8-K disclosing this Agreement and the
transactions contemplated hereby within 10 business days after the Closing Date.
Throughout the Registration Period (as defined in the Registration Rights
Agreement), the Company will use its commercially reasonable efforts to timely
file all reports, schedules, forms, statements and other documents required to
be filed by it with the SEC under the reporting requirements of the Exchange
Act, and the Company will not terminate its status as an issuer required to file
reports under the Exchange Act even if the Exchange Act or the rules and
regulations thereunder would permit such termination. The Company currently
meets, and will take all reasonably necessary action to continue to meet, the
"registrant eligibility" requirements set forth in the general instructions to
Form S-3.

                                       8
<PAGE>

     4.4  Expenses.  The Company and each Investor is liable for, and will pay,
          --------
its own expenses incurred in connection with the negotiation, preparation,
execution and delivery of this Agreement and the other agreements to be executed
in connection herewith, including, without limitation, attorneys' and
consultants' fees and expenses.

     4.5  Financial Information.  The Company agrees to send to each Investor
          ---------------------
those reports which it generally sends to holders of its Common Stock until such
Investor transfers, assigns or sells all of its Securities.

     4.6  Listing.  On or before the tenth business day after the date of this
          -------
Agreement, the Company will use its commercially reasonable efforts to secure
the listing of the Securities upon each national securities exchange or
automated quotation system, if any, upon which shares of Common Stock are then
listed (subject to official notice of issuance) and, so long as any Investor
owns any of the Securities, will use its commercially reasonable efforts
maintain such listing of the Securities.  The Company will use its commercially
reasonable efforts to obtain and, so long as any Investor owns any of the
Securities, maintain the listing and trading of its Common Stock on Nasdaq, or
the American Stock Exchange or the New York Stock Exchange and will use its
commercially reasonable efforts to comply in all respects with the Company's
reporting, filing and other obligations under the bylaws or rules of the
National Association of Securities Dealers, Inc. and such exchanges, as
applicable.

     4.7  No Integration.  The Company will not make any offers or sales of any
          --------------
security (other than the Securities) under circumstances that would cause the
offering of Securities to be integrated with any other offering of securities by
the Company (i) for the purpose of any stockholder approval provision applicable
to the Company or its securities or (ii) for purposes of any registration
requirement under the Securities Act.

                                       9
<PAGE>

     4.8  Sales by Investors.  Each Investor will sell any Securities sold by it
          ------------------
in compliance with applicable prospectus delivery requirements, if any, or
otherwise in compliance with the requirements for an exemption from registration
under the Securities Act and the rules and regulations promulgated thereunder.
No Investor will make any sale, transfer or other disposition of the Securities
in violation of federal or state securities laws.

                                   ARTICLE V
                TRANSFER AGENT INSTRUCTIONS; REMOVAL OF LEGENDS

     5.1  Issuance of Certificates.  The Company will instruct its transfer
          ------------------------
agent to issue certificates, registered in the name of each Investor or its
nominee, for the Securities. All such certificates will bear the restrictive
legend described in Section 2.7, except as otherwise specified in this Article
V. The Company will not give to its transfer agent any instruction other than as
described in this Article V and stop-transfer instructions to give effect to
Section 2.7 hereof (prior to registration of the Securities under the Securities
Act). Nothing in this Section will affect in any way the Investor's obligations
and agreement set forth in Sections 2.6 and 2.7 hereof to resell the Securities
pursuant to an effective registration statement or in compliance with an
exemption from the registration requirement of applicable securities laws.

     5.2  Unrestricted Securities.  If, unless otherwise required by applicable
          -----------------------
state securities laws, (a) the Securities represented by a certificate have been
registered under an effective registration statement filed under the Securities
Act, (b) a holder of Securities provides the Company and the Transfer Agent with
an opinion of counsel, in form, substance and scope customary for opinions of
counsel in comparable transactions, to the effect that a public sale or transfer
of such Securities may be made without registration under the Securities Act and
such sale either has occurred or may occur without restriction on the manner of
such sale or transfer, (c) such holder provides the Company and the Transfer
Agent with reasonable assurances that such Securities can be sold under Rule
144, or (d) the Securities represented by a certificate can be sold without
restriction as to the number of securities sold under Rule 144(k), the Company
will permit the transfer of the Securities, and the Transfer Agent will issue
one or more certificates, free from any restrictive legend, in such name and in
such denominations as specified by such holder. In the event that the
restrictive legend is removed from any of the certificates for the Securities
and thereafter the effectiveness of a registration statement covering such
Securities is suspended or terminated or the Company determines that a
supplement or amendment thereto is required by applicable securities laws, then
upon a reasonable advance notice to the Investor the Company may require that
the restrictive legend be placed on any certificates for the Securities that
cannot be sold pursuant to an effective registration statement or under Rule
144, and each Investor shall cooperate in the replacement of such legend. Such
legend shall thereafter be removed when such Securities may again be sold
pursuant to an effective registration statement or Rule 144.

                                  ARTICLE VI
                CONDITIONS TO THE COMPANY'S OBLIGATION TO SELL

     The obligation of the Company to issue and sell the Securities to each
Investor at the Closing is subject to the satisfaction by such Investor, on or
before the Closing Date, of each of

                                       10
<PAGE>

the following conditions. These conditions are for the Company's sole benefit
and may be waived by the Company at any time in its sole discretion:

     6.1  The Investor will have executed this Agreement and the Registration
Rights Agreement and will have delivered those agreements to the Company.

     6.2  The Investor will have delivered the purchase price for the Securities
to the Company in accordance with this Agreement.

     6.3  The representations and warranties of the Investor must be true and
correct in all material respects as of the Closing Date as though made at that
time (except for representations and warranties that speak as of a specific
date, which representations and warranties must be correct as of such date), and
the Investor will have performed and complied in all material respects with the
covenants and conditions required by this Agreement to be performed or complied
with by the Investor at or prior to the Closing. The Company must have received
a certificate or certificates dated as of the Closing Date and executed by the
Investor or a duly authorized officer of the Investor certifying as to the
matters contained in this Section 6.3.

     6.4  No statute, rule, regulation, executive order, decree, ruling or
injunction will have been enacted, entered, promulgated or endorsed by or in any
court or governmental authority of competent jurisdiction or any self-regulatory
organization having authority over the matters contemplated hereby which
prohibits the consummation of any of the transactions contemplated by this
Agreement.

                                  ARTICLE VII
              CONDITIONS TO THE INVESTOR'S OBLIGATION TO PURCHASE

     The obligation of each Investor hereunder to purchase the Securities from
the Company at the Closing is subject to the satisfaction, on or before the
Closing Date, of each of the following conditions.  These conditions are for
each Investor's respective benefit and may be waived by any Investor at any time
in its sole discretion:

     7.1  The Company will have executed this Agreement and the Registration
Rights Agreement and will have delivered those Agreements to the Investor.

     7.2  The Company will have delivered to the Investors duly executed
certificates representing the Securities in the amounts specified in Section
1.1 hereof.

     7.3  The representations and warranties of the Company must be true and
correct in all material respects as of the Closing as though made at that time
(except for representations and warranties that speak as of a specific date,
which representations and warranties must be true and correct as of such date)
and the Company must have performed and complied in all material respects with
the covenants and conditions required by this Agreement to be performed or
complied with by the Company at or prior to the Closing. The Investor must have
received a certificate or certificates dated as of the Closing Date and executed
by the Chief Executive Officer or the Chief Financial Officer of the Company
certifying as to the matters contained in this Section 7.3 and as to such other
matters as may be reasonably requested by such Investor, including, but not
limited to, the Company's Articles of Incorporation, as amended, By-laws, as

                                       11
<PAGE>

amended, Board of Directors' resolutions relating to the transactions
contemplated hereby and the incumbency and signatures of each of the officers of
the Company who may execute on behalf of the Company any document delivered at
the Closing.

     7.4  No litigation, statute, rule, regulation, executive order, decree,
ruling or injunction will have been enacted, entered, promulgated or endorsed by
or in any court or governmental authority of competent jurisdiction or any self-
regulatory organization having authority over the matters contemplated hereby
which prohibits the consummation of any of the transactions contemplated by this
Agreement.

     7.5  Trading and listing of the Common Stock on Nasdaq must not have been
suspended by the SEC or Nasdaq.

     7.6  The Investors will have received an opinion of the Company's general
counsel, dated as of the Closing Date, in form, scope and substance reasonably
satisfactory to the Investors and in substantially the form attached hereto as
Exhibit B.
---------

     7.7  The Company shall have delivered evidence reasonably satisfactory to
the Investors that the Company's transfer agent has agreed to act in accordance
with irrevocable instructions in the form attached hereto as Exhibit C.
                                                             ---------

                                 ARTICLE VIII
                                  DEFINITIONS

     8.1  "Banks" means Bay Area Bank, Bay Bank of Commerce, Cupertino National
Bank, Golden Gate Bank, Mt. Diablo National Bank, Mid-Peninsula Bank and
Peninsula Bank of Commerce.

     8.2  "Closing" means the closing of the purchase and sale of the Securities
under this Agreement.

     8.3  "Closing Date" has the meaning set forth in Section 1.3.

     8.4  "Common Stock" means the common stock, no par value per share, of the
Company.

     8.5  "Company" means Greater Bay Bancorp.

     8.6  "Exchange Act" means the Securities Exchange Act of 1934, as amended.

     8.7   "Investors" means the investors whose names are set forth on the
signature pages of this Agreement.

     8.8  "Material Adverse Effect" means a material adverse effect on (a) the
business, operations, assets or financial condition of the Company on a
consolidated basis or (b) the ability of the Company to perform its obligations
pursuant to the transactions contemplated by this Agreement or under the
agreements or instruments to be entered into or filed in connection herewith.

                                       12
<PAGE>

     8.9  "Nasdaq" means the Nasdaq National Market System.

     8.10  "Registration Rights Agreement" means the Registration Rights
Agreement, dated as of the date of this Agreement and among the parties to this
Agreement, in the form attached hereto as Exhibit A.
                                          ---------

     8.11  "Regulation D" means Regulation D as promulgated under by the SEC
under the Securities Act.

     8.12  "Rule 144" and "Rule 144(k)" mean Rule 144 and Rule 144(k),
respectively, promulgated under the Securities Act, or any successor rule.

     8.13  "SEC" means the United States Securities and Exchange Commission.

     8.14  "SEC Documents" has the meaning set forth in Section 3.6.

     8.15  "Securities" means the Common Stock sold pursuant to this Agreement.

     8.16  "Securities Act" means the Securities Act of 1933, as amended, and
the rules and regulations thereunder, or any similar successor statute.

                                  ARTICLE IX
                         GOVERNING LAW; MISCELLANEOUS

     9.1  Governing Law; Jurisdiction.  This Agreement will be governed by and
          ---------------------------
interpreted in accordance with the laws of the State of California without
regard to the principles of conflict of laws.  The parties hereto hereby submit
to the exclusive jurisdiction of the United States federal and state courts
located in the State of California with respect to any dispute arising under
this Agreement, the agreements entered into in connection herewith or the
transactions contemplated hereby or thereby.

     9.2  Counterparts; Signatures by Facsimile.  This Agreement may be
          -------------------------------------
executed in two or more counterparts, all of which are considered one and the
same agreement and will become effective when counterparts have been signed by
each party and delivered to the other parties. This Agreement, once executed by
a party, may be delivered to the other parties hereto by facsimile transmission
of a copy of this Agreement bearing the signature of the party so delivering
this Agreement. In the event any signature is delivered by facsimile
transmission, the party using such means of delivery shall cause the manually
executed pages to be physically delivered to the other party within five
business days of the execution hereof.

     9.3  Headings.  The headings of this Agreement are for convenience of
          --------
reference only, are not part of this Agreement and do not affect its
interpretation.

     9.4  Severability.  If any provision of this Agreement is invalid or
          ------------
unenforceable under any applicable  statute or rule of law, then such provision
will be deemed modified in order to conform with such statute or rule of law.
Any provision hereof that may prove invalid or

                                       13
<PAGE>

unenforceable under any law will not affect the validity or enforceability of
any other provision hereof.

     9.5  Entire Agreement; Amendments.  This Agreement and the Registration
          ----------------------------
Rights Agreement (including all schedules and exhibits thereto) constitute the
entire agreement among the parties hereto with respect to the subject matter
hereof and thereof. There are no restrictions, promises, warranties or
undertakings, other than those set forth or referred to herein or therein. This
Agreement supersedes all prior agreements and understandings among the parties
hereto with respect to the subject matter hereof. No provision of this Agreement
may be waived or amended other than by an instrument in writing signed by the
party to be charged with enforcement.

     9.6  Notices.  Any notices required or permitted to be given under the
          -------
terms of this Agreement must be sent by certified or registered mail (return
receipt requested) or delivered personally or by courier (including a recognized
overnight delivery service) or by facsimile and will be effective five days
after being placed in the mail, if mailed by regular U.S. mail, or upon receipt,
if delivered personally, by courier (including a recognized overnight delivery
service) or by facsimile, in each case addressed to a party. The addresses for
such communications are:

     If to the Company:  Greater Bay Bancorp
                         2860 West Bayshore Road
                         Palo Alto, California 94303
                         Attention:  Steven C. Smith
                         Facsimile:  (415) 494-9220


     With a copy to:     Greater Bay Bancorp
                         400 Emerson Street, 3rd Floor
                         Palo Alto, California 94301
                         Attention:  Linda M. Iannone, Esq.
                         Facsimile:  (650) 473-9419

                                      and

                         Manatt, Phelps & Phillips, LLP
                         11355 W. Olympic Boulevard
                         Los Angeles, CA 90064
                         Attention:  William T. Quicksilver, Esq.
                         Facsimile:  (310) 312-4224

     If to an Investor:  To the address set forth immediately below such
Investor's name on the signature pages hereto.

     Each party will provide written notice to the other parties of any change
in its address.

     9.7  Successors and Assigns.  This Agreement is binding upon and inures to
          ----------------------
the benefit of the parties and their successors and assigns. The Company will
not assign this Agreement or any rights or obligations hereunder without the
prior written consent of the Investors, and no Investor may assign this
Agreement or any rights or obligations hereunder without the prior written
consent of the Company. Notwithstanding the foregoing, an Investor may assign
all or

                                       14
<PAGE>

part of its rights and obligations hereunder to any of its "affiliates," as that
term is defined under the Securities Act, without the consent of the Company so
long as the affiliate is an accredited investor (within the meaning of
Regulation D under the Securities Act) and agrees in writing to be bound by this
Agreement.

     9.8  Third-Party Beneficiaries.  This Agreement is intended for the benefit
          -------------------------
of the parties hereto and their respective permitted successors and assigns, and
is not for the benefit of, nor may any provision hereof be enforced by, any
other person.

     9.9  Survival.  The representations and warranties of the Company and the
          --------
agreements and covenants set forth herein will survive the Closing hereunder.
The Company makes no representations or warranties in any oral or written
information provided to Investors, other than the representations and warranties
included herein.

     9.10  Further Assurances.  Each party will do and perform, or cause to be
           ------------------
done and performed, all such further acts and things, and will execute and
deliver all other agreements, certificates, instruments and documents, as
another party may reasonably request in order to carry out the intent and
accomplish the purposes of this Agreement and the consummation of the
transactions contemplated hereby.

     9.11  No Strict Construction.  The language used in this Agreement is
           ----------------------
deemed to be the language chosen by the parties to express their mutual intent,
and no rules of strict construction will be applied against any party.

     9.12  Equitable Relief.  Each party acknowledges that a breach by it or its
           ----------------
obligations hereunder will cause irreparable harm to the other parties by
vitiating the intent and purposes of the transactions contemplated hereby.
Accordingly, each party acknowledges that the remedy at law for a breach of its
obligations hereunder will be inadequate and agrees, in the event of a breach of
threatened by such party of the provisions of this Agreement, that the other
party shall be entitled, in addition to all other available remedies, to
temporary and permanent injunctive relief in any such case without the necessity
of proving actual damages.

        [The remainder of this page has been intentionally left blank]

                                       15
<PAGE>

     IN WITNESS WHEREOF, the undersigned Investors and the Company have caused
this Agreement to be duly executed as of the date first above written.

                              COMPANY:

                              GREATER BAY BANCORP

                              By: /s/ Steven C. Smith
                                  -------------------
                                  Name:   Steven C.  Smith
                                  Title:  Executive Vice President,
                                          Chief Administrative Officer
                                          and Chief Financial Officer


                      [Signatures continued on next page]

                                       16
<PAGE>

                              Investor: FRANKLIN SMALLCAP GROWTH FUND
                              --------

                              By:  /s/ Murray L. Simpson
                                   --------------------------------

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

                              Name:  Murray L. Simpson
                                     ------------------------------

                              Title  Vice President
                                     ------------------------------

                              Shares of Common Stock: 201,200
                                                      -------------

                              Aggregate Purchase Amount: $2,944,400
                                                         ----------


                              Investor: Emerging Small Company Trust
                              --------

                              By:  /s/ Murray L. Simpson
                                   --------------------------------

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

                              Name:  Murray L. Simpson
                                     ------------------------------

                              Title  Vice President
                                     ------------------------------

                              Shares of Common Stock: 7,900
                                                      -------------

                              Aggregate Purchase Amount: $292,300
                                                         ----------


                              Investor: U.S. SMALLCAP FUND
                              --------

                              By:  /s/ Murray L. Simpson
                                   --------------------------------

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

                              Name:  Murray L. Simpson
                                     ------------------------------

                              Title  Vice President
                                     ------------------------------

                              Shares of Common Stock: 1,700
                                                      -------------

                              Aggregate Purchase Amount: $62,900
                                                         ----------


                              Investor: FRANKLIN SMALLCAP INVESTMENTS FUND
                              --------

                              By:  /s/ Murray L. Simpson
                                   --------------------------------

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

                              Name:  Murray L. Simpson
                                     ------------------------------

                              Title  Vice President
                                     ------------------------------

                              Shares of Common Stock: 1,700
                                                      -------------

                              Aggregate Purchase Amount: $62,900
                                                         ----------


                              Investor: MERRILL LYNCH GLOBAL FINANCIAL SERVICES
                              --------
                                        PORTFOLIO, INC.

                              By:  /s/ James Ellman
                                   --------------------------------

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

                              Name:  James Ellman
                                     ------------------------------

                              Title  Vice President and Portfolio Manager
                                     ------------------------------------

                              Shares of Common Stock: 7,000
                                                      -------------

                              Aggregate Purchase Amount: $
                                                         ----------


                                       17
<PAGE>

                              Investor: MERRILL LYNCH EQUITY CONVERTIBLE SERIES-
                              --------
                                        FINANCIAL SERVICES PORTFOLIO

                              By:  /s/ James Ellman
                                   --------------------------------

                              -------------------------------------
                              Name:  James Ellman
                                     ------------------------------
                              Title  Portfolio Manager
                                     ------------------------------
                              Shares of Common Stock: 15,500
                                                      -------------
                              Aggregate Purchase Amount: $
                                                          ---------


                              Investor: LAWRENCE OFFSHORE PARTNERS, LLC
                              --------

                              By:  /s/ Lawrence Garshofsky
                                       ----------------------------

                              -------------------------------------
                              Name:  Lawrence Garshofsky
                                     ------------------------------
                              Title: Manager
                                     ------------------------------
                              Shares of Common Stock: 2,500
                                                      -------------
                              Aggregate Purchase Amount: $92,500
                                                         ----------


                              Investor: LAWRENCE PARTNERS, LP
                              --------

                              By:  /s/ Lawrence Garshofsky
                                   --------------------------------

                              -------------------------------------
                              Name:  Lawrence Garshofsky
                                     ------------------------------
                              Title: Manager
                                     ------------------------------
                              Shares of Common Stock: 2,500
                                                      -------------
                              Aggregate Purchase Amount: $92,500
                                                         ----------


                              Investor: SUNOVA LONG-TERM OPPORTUNITY FUND, LP
                              --------

                              By:  /s/ Matthew Byrnes
                                   --------------------------------

                              -------------------------------------
                              Name:  Matthew Byrnes
                                     ------------------------------
                              Title: Managing Partner
                                     ------------------------------
                              Shares of Common Stock: 9,000
                                                      -------------
                              Aggregate Purchase Amount: $333,000
                                                         ----------


                              Investor: MALTA OFFSHORE, LTD.
                              --------
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   --------------------------------

                              -------------------------------------
                              Name:  Terry Maltese
                                     ------------------------------
                              Title: President
                                     ------------------------------
                              Shares of Common Stock: 900
                                                      -------------
                              Aggregate Purchase Amount: $33,300
                                                         ----------

                                       18
<PAGE>

                              Investor: MALTA HEDGE FUND II, LP
                              --------
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   --------------------------------

                              -------------------------------------
                              Name:  Terry Maltese
                                     ------------------------------
                              Title  President
                                     ------------------------------
                              Shares of Common Stock: 3,600
                                                      --------------
                              Aggregate Purchase Amount: $133,200
                                                         -----------


                              Investor: MALTA HEDGE FUND, LP
                              --------
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   --------------------------------

                              -------------------------------------
                              Name:  Terry Maltese
                                     ------------------------------
                              Title: President
                                     ------------------------------
                              Shares of Common Stock: 900
                                                      -------------
                              Aggregate Purchase Amount: $33,300
                                                         ----------


                              Investor: MALTA PARTNERS II, LP
                              --------
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   --------------------------------

                              -------------------------------------
                              Name:  Terry Maltese
                                     ------------------------------
                              Title: President
                                     ------------------------------
                              Shares of Common Stock: 2,700
                                                      -------------
                              Aggregate Purchase Amount: $99,900
                                                        -----------

                              Investor: MALTA PARTNERS, LP
                              --------
                                        SANDLER O'NEILL ASSET MANAGEMENT

                              By:  /s/ Terry Maltese
                                   --------------------------------

                              -------------------------------------
                              Name:  Terry Maltese
                                     ------------------------------
                              Title: President
                                     ------------------------------
                              Shares of Common Stock: 900
                                                      -------------
                              Aggregate Purchase Amount: $33,300
                                                         ----------


                              Investor: NORTHAVEN PARTNERS, L.P.
                              --------

                              By:  /s/ Paul Burke
                                   --------------------------------

                              -------------------------------------
                              Name:  Paul Burke
                                     ------------------------------
                              Title: Member of General Partner
                                     ------------------------------
                              Shares of Common Stock: 4,100
                                                      -------------
                              Aggregate Purchase Amount: $151,700
                                                         ----------

                                       19
<PAGE>

                              Investor: NORTHAVEN PARTNERS II, L.P.
                              --------

                              By: /s/ Paul Burke
                                  ---------------------------------

                              -------------------------------------
                              Name: Paul Burke
                                    -------------------------------
                              Title Member of GP
                                    -------------------------------
                              Shares of Common Stock: 6,900
                                                      -------------
                              Aggregate Purchase Amount: $255,300
                                                          ---------


                              Investor: NORTHAVEN PARTNERS, III, L.P.
                              --------

                              By: /s/ Paul Burke
                                  ---------------------------------

                              -------------------------------------
                              Name: Paul Burke
                                    -------------------------------
                              Title Member of GP
                                    -------------------------------
                              Shares of Common Stock: 5,000
                                                      -------------
                              Aggregate Purchase Amount: $185,000
                                                          ---------


                              Investor: BANC FUND V, L.P.
                              --------

                              By: /s/ Charles J. Moore
                                  ---------------------------------

                              -------------------------------------
                              Name: Charles J. Moore
                                    -------------------------------
                              Title Member
                                    -------------------------------
                              Shares of Common Stock: 10,000
                                                      -------------
                              Aggregate Purchase Amount: $370,000
                                                          ---------


                              Investor: BANK FUND III TRUST
                              --------

                              By: /s/ Charles J. Moore
                                  ---------------------------------

                              -------------------------------------
                              Name: Charles J. Moore
                                    -------------------------------
                              Title Member
                                    -------------------------------
                              Shares of Common Stock: 7,784
                                                      -------------
                              Aggregate Purchase Amount: $288,008
                                                          ---------

                              Investor: BANC FUND III, L.P.
                              --------

                              By:  /s/ Charles J. Moore
                                   --------------------------------

                              -------------------------------------
                              Name:  Charles J. Moore
                                     ------------------------------
                              Title: Member
                                     ------------------------------
                              Shares of Common Stock: 2,540
                                                      -------------
                              Aggregate Purchase Amount: $93,980
                                                         ----------

                              Investor: MUTUAL FINANCIAL SERVICES FUND
                              --------

                              By: /s/ Raymond Garea
                                  ---------------------------------

                              -------------------------------------
                              Name:  Raymond Garea
                                     ------------------------------
                              Title: Senior Vice President
                                     ------------------------------
                              Shares of Common Stock: 20,000
                                                      -------------
                              Aggregate Purchase Amount: $740,000
                                                         ----------

                              Investor: NICHOLAS-APPLEGATE PACIFIC CENTURY
                              --------
                                        TRUST #2 SMALL

                              BY: /s/ Scott A. Long
                                  ---------------------------------

                              -------------------------------------
                              Name:  Scott A. Long
                                     ------------------------------
                              Title: Head of Global Operations
                                     ------------------------------
                              Shares of Common Stock: 9,600
                                                      -------------
                              Aggregate Purchase Amount $355,200
                                                        -----------

                              Investor: NICHOLAS-APPLEGATE SMALL CAP VALUE
                              --------

                              BY: /s/ Scott A. Long
                                  ---------------------------------

                              -------------------------------------
                              Name:  Scott A. Long
                                     ------------------------------
                              Title: Head of Global Operations
                                     ------------------------------
                              Shares of Common Stock: 300
                                                      -------------
                              Aggregate Purchase Amount $11,100
                                                        -----------

                              Investor: NICHOLAS-APPLEGATE CORNERSTONE/SHEPERD
                                         VALUE

                              BY: /s/ Scott A. Long
                                  ---------------------------------

                              -------------------------------------
                              Name:  Scott A. Long
                                     ------------------------------
                              Title: Head of Global Operations
                                     ------------------------------
                              Shares of Common Stock: 100
                                                      -------------
                              Aggregate Purchase Amount $3,700
                                                        -----------