EXHIBIT 10.1

                             EMPLOYMENT AGREEMENT


     This Agreement is made and entered into as of January 1, 1999 by and
between GREATER BAY BANCORP ("Employer"), a California corporation and DAVID L.
KALKBRENNER ("Employee").

                                    RECITALS
                                    --------

     WHEREAS, Employer is registered as a bank holding company under the Bank
Holding Company Act of 1956, as amended, and subject to the supervision and
regulation of the Board of Governors of the Federal Reserve System ("FRB");

     WHEREAS, Employer is the sole shareholder and owner of 100% of the
outstanding capital voting stock of various subsidiary banking corporations
chartered under California and federal banking laws (collectively, the
"Subsidiary Banks");

     WHEREAS, the Subsidiary Banks are subject to the supervision and
regulation, as applicable, of the California Department of Financial
Institutions ("CDFI"), Federal Deposit Insurance Corporation ("FDIC"), FRB and
the Office of the Comptroller of the Currency ("OCC");

     WHEREAS, Employer and Employee desire to terminate that certain employment
agreement with Employee dated March 3, 1992 and as amended by amendment dated
March 27, 1998, and enter into a new employment agreement for the purposes of
engaging the services of Employee by reason of his experience, training and
ability in the commercial banking industry and to delineate the rights,
obligations and responsibilities of the Employer and Employee; and

     NOW, THEREFORE, in consideration of the mutual covenants and agreements
contained herein, the Employer and Employee agree as follows:

                                   AGREEMENT
                                   ---------

     1.  Termination of Existing Agreement/Term of Employment.  Employer and
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Employee acknowledge and agree that the existing employment agreement between
Employer's banking subsidiary, Mid-Peninsula Bank and its predecessor parent
bank holding company, Mid-Peninsula Bancorp (subsequently re-named Greater Bay
Bancorp), and Employee dated March 3, 1992 and amendment no. 1 thereto dated
March 27, 1998, is hereby terminated effective with the date of this Agreement.
Employer hereby employs Employee and Employee hereby accepts employment with
Employer, upon the terms and conditions hereinafter set forth, for a period of
five (5) years from the date hereof.

     2.  Duties and Obligations of Employee.  Employee shall serve as the
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President and Chief Executive Officer of Employer and shall perform the
customary duties of such office as may from time to time be reasonably requested
of him by the Board of Directors of Employer, in addition to the following:

 
                                      -2-

 
          (a) Voting as a member of the Board of Directors of Employer and the
Subsidiary Banks and such committees thereof as the Board of Directors of
Employer shall designate;

          (b) Participating in community affairs which are beneficial to the
Employer and the Subsidiary Banks;

          (c) Maintaining a good relationship with Employer's shareholders and
the Boards of Directors of Employer and the Subsidiary Banks;

          (d) Maintaining a good relationship with regulatory agencies and
governmental authorities having jurisdiction over Employer and the Subsidiary
Banks;

          (f) Providing leadership in planning and implementing the conduct of
business and the affairs of the Employer and the Subsidiary Banks;

          (g) Hiring and firing of all employees other than executive officers
of the Employer, subject at all times to the policies and directives set by the
Employer's Board of Directors.

     3.   Devotion to Employer's Business.
          ------------------------------- 

          (a) Employee shall devote his full business time, ability, and
attention to the business of Employer during the term of this Agreement and
shall not during the term of this Agreement engage in any other business
activities, duties, or pursuits whatsoever, or directly or indirectly render any
services of a business, commercial, or professional nature to any other person
or organization, whether for compensation or otherwise, without the prior
written consent of Employer's Board of Directors. However, the expenditure of
reasonable amounts of time for educational, charitable, or professional
activities shall not be deemed a breach of this Agreement if those activities do
not materially interfere with the services required of Employee under this
Agreement. Nothing in this Agreement shall be interpreted to prohibit Employee
from making passive personal investments. However, Employee shall not directly
or indirectly acquire, hold, or retain any interest in any business competing
with or similar in nature to the business of Employer. Employer acknowledges
that Employee currently serves as a member of the Board of Directors of Thoits
Insurance Services, Inc. and hereby consents to such service by Employee.

          (b) Employee agrees to conduct himself at all times with due regard to
public conventions and morals.  Employee further agrees not to do or commit any
act that will reasonably tend to shock or offend the community and have a
material adverse effect upon Employer.

 
          (c) Employee hereby represents and agrees that the services to be
performed under the terms of this Agreement are of a special, unique, unusual,
extraordinary, and intellectual character that gives them a peculiar value, the
loss of which cannot be reasonably or adequately compensated in damages in an
action at law. Employee therefore expressly agrees that Employer, in addition to
any other rights or remedies that Employer may possess, shall be entitled to
injunctive and other equitable relief to prevent or remedy a breach of this
Agreement by Employee.

     4.   Noncompetition by Employee.  Employee shall not, during the term of
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this Agreement, directly or indirectly, either as an employee, employer,
consultant, agent, principal, stockholder, officer, director, or in any other
individual or representative capacity, engage or participate in any competitive
banking or financial services business without the prior written consent of
Employer.

     5.   Indemnification.
          --------------- 

          (a) Employee shall indemnify and hold Employer harmless from all
liability for loss, damage, or injury to persons or property resulting from the
gross negligence or intentional misconduct of the Employee.

          (b) To the extent permitted by law, Employer shall indemnify Employee
if he was or is a party or is threatened to be made a party in any action
brought by a third party against Employee (whether or not Employer is joined as
a party defendant) against expenses, judgments, fines, settlements and other
amounts actually and reasonably incurred in connection with said action if
Employee acted in good faith and in a manner Employee reasonably believed to be
in the best interest of Employer (and with respect to a criminal proceeding if
Employee had no reasonable cause to believe his conduct was unlawful), provided
that the alleged conduct of Employee arose out of and was within the course and
scope of his employment as an officer or employee of Employer.

     6.   Disclosure of Information.  Employee shall not, either before or after
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termination of this Agreement, without the prior written consent of Employer's
Board of Directors or except as required by law to comply with legal process
including, without limitation, by oral questions, interrogatories, requests for
information or documents, subpoena, civil investigative demand or similar
process, disclose to anyone any financial information, trade or business
secrets, customer lists, computer software or other information not otherwise
publicly available concerning the business or operations of Employer and/or one
or all of the Subsidiary Banks.  Employee further recognizes and acknowledges
that any financial information concerning any customers of Employer or the
Subsidiary Banks, as it may exist from time to time, is strictly confidential
and is a valuable, special and unique asset of Employer's business.  Employee
shall not, either before or after termination of this Agreement, without such
consent or except as required by law, disclose to anyone said financial
information or any part thereof, for any reason or purpose whatsoever.  In the
event Employee is required by law to disclose such information described in this
paragraph 6, Employee will provide Employer and its respective counsel with
immediate notice of such request so that they may consider seeking a protective
order.  If in the absence of a protective order or the receipt of a waiver
hereunder Employee is nonetheless, in the written opinion of 

 
knowledgeable counsel, compelled to disclose any of such information to any
tribunal or any other party or else stand liable for contempt or suffer other
material censure or material penalty, then Employee may disclose (on an "as
needed" basis only) such information to such tribunal or other party without
liability hereunder. This paragraph 6 shall survive the expiration or
termination of this Agreement.

     7.   Written, Printed or Electronic Material.  All written, printed or
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electronic material, notebooks and records including, without limitation,
computer disks used by Employee in performing duties for Employer, other than
Employee's personal notes and diaries, are and shall remain the sole property of
Employer.  Upon termination of employment, Employee shall promptly return all
such material (including all copies, extracts and summaries thereof) to
Employer.  This paragraph 7 shall survive expiration or termination of this
Agreement.

     8.   Surety Bond.  Employee agrees that he will furnish all information and
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take any other steps necessary from time to time to enable Employer to obtain or
maintain a fidelity bond conditional on the rendering of a true account by
Employee of all monies, goods, or other property which may come into the
custody, charge, or possession of Employee during the term of his employment.
The surety company issuing the bond and the amount of the bond must be
acceptable to Employer.  All premiums on the bond shall be paid by Employer.
Employer shall have no obligation to pay severance benefits to Employee in
accordance with paragraph 16 (d) of this Agreement in the event that the
Employee's employment is terminated in connection with the Employee's failure to
qualify for a surety bond at any time during the term of this Agreement and such
failure to qualify results from an occurrence described in paragraph 16(a) (5),
(6) or (7, to the extent of an Employee breach).

     9.   Base Salary.  In consideration for the services to be performed
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hereunder, Employee shall receive a salary at the rate of Three Hundred Sixty
Thousand Dollars ($360,000) per annum, payable in substantially equal
installments during the term of this Agreement of approximately Fifteen Thousand
Dollars ($15,000.00) on the first and fifteenth days of each month, subject to
applicable adjustments for withholding taxes and prorations for any partial
employment period.  Employee shall receive such annual adjustments in salary, if
any, as may be determined by Employer's Board of Directors, in its sole
discretion.

                                      -5-

 
     10.  Salary Continuation During Disability.  If Employee for any reason
          -------------------------------------                             
(except as expressly provided below) becomes temporarily or permanently disabled
so that he is unable to perform the duties under this Agreement, Employer agrees
to pay Employee the base salary otherwise payable to Employee pursuant to
paragraph 9 of this Agreement, reduced by the amounts received by Employee from
state disability insurance, or worker's compensation or other similar insurance
benefits through policies provided by Employer, for a period of one (1) year
from the date of disability.

     For purposes of this paragraph 10, "disability" shall be defined as
provided in Employer's disability insurance program.  Notwithstanding anything
herein to the contrary, Employer shall have no obligation to make payments for a
disability resulting from the deliberate, intentional actions of Employee, such
as, but not limited to, attempted suicide or chemical dependence of Employee.

     11.  Incentive Compensation.  The Executive Committee of the Board of
          ----------------------                                          
Directors of Employer will determine the amount, if any, of pre-tax net profit
of Employer available for allocation and distribution as incentive compensation
pursuant to the executive incentive compensation program (the "Program").  Pre-
tax net profit for purposes of the determination is defined as actual pre-tax
net profit before allocation of any incentive compensation.

     Distribution of any incentive compensation pursuant to the Program shall be
made only to employees of Employer eligible to participate in the Program and
who are employed by Employer at the time of any such distribution.  Any such
distribution of incentive compensation shall be prorated for any partial year in
accordance with the terms of the Program.

     12.  Stock Options.  Employer has previously granted stock options to the
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Employee and the Employer may, but is not obligated to, grant additional stock
options to the Employee in the future.  Any such grants shall be evidenced by a
Stock Option Agreement entered into between Employer and Employee and a copy of
each such Stock Option Agreement shall be attached to this Agreement as an
exhibit.  Notwithstanding any contrary provision of any such Stock Option
Agreement or any related Stock Option Plan of Employer, no rights of employment
shall be conferred upon Employee or result from any such Stock Option Agreement
or Stock Option Plan of Employer.  Any employment rights and corresponding
duties of Employee pursuant to his employment by Employer shall be limited to
and interpreted solely in accordance with the terms and provisions of this
Agreement.

     13.  Other Benefits.  Employee shall be entitled to those employee benefits
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adopted by Employer for all employees of Employer, subject to applicable
qualification requirements and regulatory approval requirements, if any.
Employee shall be further entitled to the 

                                      -6-

 
following additional benefits which shall supplement or replace, to the extent
duplicative of any part or all of the general employee benefits, the benefits
otherwise provided to Employee:

          (a)  Vacation.  Employee shall be entitled to five (5) weeks annual 
               --------    
vacation leave at his then existing rate of full salary each year during the
term of this Agreement. Employee may be absent from his employment for vacation
as long as such leave is reasonable and does not jeopardize his responsibilities
and duties specified in this Agreement. The length of vacation should not exceed
two (2) weeks without the approval of Employer's Executive Committee of the
Board of Directors. Vacation time will accrue in accordance with Employer's
personnel policies.

                                      -7-

 
          (b)  Automobile Allowance and Insurance.  Employer shall pay to 
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Employee an automobile allowance of Twelve Thousand Dollars ($12,000) per year
during the term of this Agreement, payable at the rate of One Thousand Dollars
($1,000) per month. Employee shall acquire or otherwise make available for his
business and personal use an automobile, suitable to his position, and (i)
maintain it in good condition and repair; (ii) maintain public liability
insurance and property damage insurance policies with insurer(s) acceptable to
Employer and such coverages in such amounts as may be acceptable to Employer
from time to time; and (iii) such policies shall name Employer as an additional
insured, subject to the requirement that Employee's allowance described above
shall be increased in an amount equal to the additional premium expense, if any,
resulting from Employer being named as an additional insured. Employer may, in
its sole discretion, elect to provide and pay for such insurance policies in
lieu of Employee maintaining such policies.

          (c)  Personal Insurance.  Employer shall provide during the term of 
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this Agreement at Employer's sole cost, policies of universal life insurance in
the amount of Five Hundred Thousand Dollars ($500,000) and group life, health
(including medical, dental and hospitalization), accident and disability
insurance coverage for Employee and his dependents through a policy or policies
provided by insurer(s) selected by Employer in its sole discretion.

          (d)  Supplemental Compensation.  Employer shall provide as soon as
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practicable, but not later than March 31, 1999 unless extended by written
consent of Employee, an agreement satisfactory to Employee providing
supplemental compensation benefits to Employee payable upon retirement or as
otherwise set forth in such agreement.  Employee agrees to waive any rights
under his existing Salary Continuation Agreement between Employer's banking
subsidiary, Mid-Peninsula Bank, and Employee dated April 26, 1995, as a
condition to the effectiveness of such supplemental compensation benefits
agreement.

     14.  Annual Physical Examination.  Employer shall pay or reimburse Employee
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for the cost of an annual physical examination conducted by a California
licensed physician selected by Employee and reasonably acceptable to Employer.
Employee shall report the general substance of the physician's overall
evaluation of Employee's physical condition to the Employer's Executive
Committee of the Board of Directors of Employer as soon as reasonably
practicable following Employee's receipt of such information from the physician.

 
     15.  Business Expenses.  Employee shall be reimbursed for all ordinary and
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necessary expenses incurred by Employee in connection with his employment.
Employee shall also be reimbursed for expenses incurred in activities associated
with promoting the business of Employer, including expenses for club
memberships, entertainment, travel and other expenses for attendance at
conventions and education programs, and similar items.   Employer will pay for
or will reimburse Employee for such expenses upon presentation by Employee from
time to time of receipts or other appropriate evidence of such expenditures.
Any club memberships shall be approved in advance of purchase by the Employer's
Executive Committee of the Board of Directors (the "Executive Committee").
During the term of this Agreement, Employee shall have an option to purchase any
club memberships from the Employer if the Executive Committee decides to
terminate any such membership.  Upon termination of employment, the Employee
shall have an option to purchase any club memberships from the Employer during
the six (6) month period following such termination.  Any purchase by Employee
from Employer of a club membership, either during the term of this Agreement or
upon termination of employment, shall be at the same purchase price paid by the
Employer to acquire each club membership, unless otherwise agreed by the
Executive Committee.

     16.  Termination of Agreement.
          ------------------------ 

          (a) Automatic Termination.  This Agreement shall terminate 
              ---------------------         
automatically without further act of the parties and immediately upon the
occurrence of any one of the following events, subject to either party's right,
without any obligation whatsoever, to waive an event reasonably susceptible of
waiver, and the obligation of Employer to pay the amounts which would otherwise
be payable to Employee under this Agreement through the end of the month in
which the event occurs, except that only in the event of termination based upon
subparagraphs (1), (4) or (7, to the extent of Employer's breach) below shall
Employee be entitled to receive severance payments pursuant to paragraph 16 (d)
of this Agreement:

               (1)  The occurrence of circumstances that make it impossible or
                    impractical for Employer to conduct or continue its
                    business.

               (2)  The death of Employee.

               (3)  The loss by Employee of legal capacity.

               (4)  The loss by Employer of legal capacity to contract.

               (5)  Employee's deliberate violation of (i) any state or federal
                    banking or securities laws, or the Bylaws, rules, policies
                    or resolutions of the Employer, or (ii) the rules or
                    regulations of the CDFI, FDIC, FRB or OCC, or other
                    regulatory agency or governmental authority having
                    jurisdiction over the Employer and/or the Subsidiary Banks,
                    which has a material adverse effect upon the Employer and/or
                    the Subsidiary Banks.

               (6)  Employee's conviction of any felony which has a material
                    adverse effect upon Employer.

 
               (7)  Either party breaches the terms or provisions of this
                    Agreement and such breach has a material adverse effect upon
                    the non-breaching party.

                                     -10-

 
          (b) Termination by Employer.  Employer may, at its election and in its
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sole discretion, terminate this Agreement for any reason, or for no reason, by
giving not less than thirty (30) days' prior written notice of termination to
Employee, without prejudice to any other remedy to which Employer may be
entitled either at law, in equity or under this Agreement.  Upon such
termination, Employee shall be entitled to receive any employment benefits which
shall have accrued prior to such termination and the severance pay specified in
paragraph 16 (d) below.

          (c) Termination by Employee.  This Agreement may be terminated by
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Employee for any reason, or no reason, by giving not less than thirty (30) days'
prior written notice of termination to Employer.  Upon such termination, all
rights and obligations accruing to Employee under this Agreement shall cease,
except that such termination shall not prejudice Employee's rights regarding
employment benefits which shall have accrued prior to such termination and any
other remedy which Employee may have at law, in equity or under this Agreement,
which remedy accrued prior to such termination.

          (d) Severance Pay - Termination by Employer.  In the event of
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termination by Employer pursuant to paragraph 16 (b) or automatic termination
based upon paragraph 16 (a) (1), (4) or (7, to the extent of Employer's breach)
of this Agreement, Employee shall be entitled to receive severance pay at
Employee's rate of salary immediately preceding such termination equal to
thirty-six (36) months' salary (in addition to incentive compensation or bonus
payments due Employee, if any), payable in substantially equal monthly
installments on the first and fifteenth days of each month for a period of
thirty-six (36) months.  Notwithstanding the foregoing, in the event of a
"change in control" as defined in subparagraph (e) below, Employee shall not be
entitled to severance pay pursuant to this subparagraph (d) and any rights of
Employee to severance pay shall be limited to such rights as are specified in
subparagraph (e) below.  Employee acknowledges and agrees that severance pay
pursuant to this subparagraph (d) is in lieu of all damages, payments and
liabilities on account of the early termination of this Agreement and the sole
and exclusive remedy for Employee terminated at the will of Employer pursuant to
paragraph 16(b) or pursuant to certain provisions of paragraph 16 (a) described
herein.

          (e) Severance Pay - Change in Control.  In the event of a "change in
              ---------------------------------                               
control" as defined herein and within a period of three (3) years following
consummation of such a change in control (i) Employee's employment is
terminated; or (ii) any adverse change occurs in the nature and scope of
Employee's position, responsibilities, duties, salary, benefits or location of
employment; or (iii) any event occurs which reasonably constitutes a demotion,
significant diminution or constructive termination (by resignation or otherwise)
of Employee's employment, Employee shall be entitled to receive severance pay in
addition to any bonus or incentive compensation payments due Employee.  Any such
severance pay due Employee shall be in an amount equal to two and ninety-nine
one hundredths (2.99) times Employee's average annual compensation for the five
(5) years immediately preceding the change in control.  Employee's average
annual compensation shall be determined by the product of the average of the
aggregate compensation paid by Employer to Employee which was includable in
Employee's gross income for federal income tax purposes for the five (5) tax
years ending immediately prior to the change in control divided by five (5).  If
Employee was employed by Employer for fewer than five (5) years immediately
preceding the change in control,

 
Employee's average annual compensation shall be determined by the product of the
aggregate compensation paid to Employee by Employer and includable in Employee's
gross income for federal income tax purposes for the years less than such five
(5) year period that Employee was employed by Employer preceding the change in
control divided by the aggregate number of such years less than the five (5)
year period.

          In addition to the change in control severance payment rights of
Employee described above and notwithstanding any other provisions of this
Agreement, Employee shall be entitled to receive the severance payments
specified in this paragraph 16 (e) in the event that Employee voluntarily
terminates his employment with Employer or its successor effective on a date
within the thirty (30) day period immediately after the expiration of the sixth
month following a change in control. Employee shall deliver written notice to
Employer of his intention to terminate employment specifying the effective date
within such thirty (30) day period described above, which notice must be
received by Employer not less than twenty (20) days prior to the expiration of
the sixth month following such a change in control.

          If all or any portion of the amounts payable to the Employee under
this Agreement, either alone or together with other payments which the Employee
has the right to receive from the Employer, constitute "excess parachute
payments" within the meaning of Section 280G of the Internal Revenue Code of
1986, as amended (the "Code"), that are subject to the excise tax imposed by
Section 4999 of the Code (or similar tax and/or assessment), the Employer (and
its successor) shall increase the amounts payable under this Agreement to the
extent necessary to afford the Employee substantially the same economic benefit
under this Agreement as the Employee would have received had no such excise tax
been imposed on the payments due the Employee under this Agreement.  The
determination of the amount of any such excise taxes shall be made initially by
the independent accounting firm employed by the Employer immediately prior to
the occurrence of the event constituting a change in control.

          If, at a later date, it is determined (pursuant to final regulations
or published rulings of the Internal Revenue Service, final judgment of a court
of competent jurisdiction, or otherwise) that the amount of excise taxes payable
to the Employee is greater than the amount initially so determined, then the
Employer (or its successor) shall pay to the Employee an amount equal to the sum
of such additional excise taxes and any interest, fines and penalties resulting
from such underpayment, plus an amount necessary to reimburse the Employee
substantially for any income, excise or other taxes payable by the Employee with
respect to such amounts.

                                      -12-

 
          Any such severance shall be payable in substantially equal monthly
installments on the first and fifteenth days of each month for a period of
thirty-six (36) months. Such severance payments, if any, shall be in lieu of all
damages, payments and liabilities on account of the events described above for
which such severance payments, if any, may be due Employee and any severance
payment rights of Employee under paragraph 16 (d) of this Agreement. This
subparagraph (e) shall be binding upon and inure to the benefit of the parties
and any successors or assigns of Employer or any "person" as defined herein.

                                      -13-

 
          Notwithstanding the foregoing, Employee shall not be entitled to
receive nor shall Employer, its successors, assigns or any "person" as defined
herein be obligated to pay severance payments pursuant to this subparagraph (e)
in the event of an occurrence described in paragraph 16 (a)(5), (6) or (7, to
the extent of an Employee breach), or in the event Employee terminates
employment in accordance with paragraph 16 (c) and the termination is not a
result of or based upon the occurrence of any event described in paragraph 16
(e)(ii) or (iii) above or a voluntary termination within the thirty (30) day
period immediately after the expiration of the sixth month following a change in
control as described above.

          17.  Change in Control Definition.  The term "change in control"
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shall mean the first to occur of any of the following events with respect to the
Employer:

          (a)  Any "person" (as such term is used in sections 13 and 14(d)(2) of
the Securities Exchange Act of 1934, as amended (the "Exchange Act"), which
becomes the beneficial owner (as that term is used in section 13(d) of the
Exchange Act), directly or indirectly, of twenty-five percent (25%) or more of
the Employer's capital stock entitled to vote in the election of directors,
other than a group of two or more persons not (i) acting in concert for the
purpose of acquiring, holding or disposing of such stock or (ii) otherwise
required to file any form or report with any governmental agency or regulatory
authority having jurisdiction over the Employer which requires the reporting of
any change in control;

          (b)  During any period of not more than two (2) consecutive years, not
including any period prior to the date of this Agreement, individuals who, at
the beginning of such period, constitute the Board of Directors of the Employer,
and any new director (other than a director designated by a person who has
entered into an agreement with the Employer to effect a transaction described in
paragraph 17 (a), (c), (d) or (e) of this subparagraph 1.4) whose appointment to
the Board of Directors or nomination for election to the Board of Directors was
approved by a vote of at least three-fourths (3/4ths) of the directors then
still in office, either were directors at the beginning of such period or whose
appointment or nomination for election was previously so approved, cease for any
reason to constitute at least a majority thereof;

          (c)  The effective date of any consolidation or merger of the Employer
(after all requisite shareholder, applicable regulatory and other approvals and
consents have been obtained), other than a consolidation or merger of the
Employer in which the holders of the voting capital stock of the Employer
immediately prior to the consolidation or merger hold more than fifty percent
(50%) of the voting capital stock of the surviving entity immediately after the
consolidation or merger;

          (d)  The shareholders of the Employer approve any plan or proposal for
the liquidation or dissolution of the Employer; or

          (e)  The shareholders of the Employer approve the sale or transfer of
substantially all of the Employer's assets to parties that are not within a
"controlled group of corporations" (as that term is defined in section 1563 of
the Code) in which the Employer is a member.

     18.  Notices.  Any notices to be given hereunder by either party to the
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other shall be in writing and may be transmitted by personal delivery or by U.S.
mail, registered or certified,

                                      -14-

 
postage prepaid with return receipt requested. Mailed notices shall be addressed
to the parties at the addresses listed as follows:

     Employer: Principal place of business

     Employee: Principal place of business as shown in Employer's Personnel
               Records and Employee's personal file.

Each party may change the address for receipt of notices by written notice in
accordance with this paragraph 18.  Notices delivered personally shall be deemed
communicated as of the date of actual receipt; mailed notices shall be deemed
communicated as of three (3) days after the date of mailing.

                                      -15-

 
     19.  Arbitration.  All claims, disputes and other matters in question
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arising out of or relating to this Agreement or the breach or interpretation
thereof, other than those matters which are to be determined by the Employer in
its sole and absolute discretion, shall be resolved by binding arbitration
before a representative member, selected by the mutual agreement of the parties,
of the Judicial Arbitration and Mediation Services, Inc., San Francisco,
California ("JAMS"), in accordance with the rules and procedures of JAMS then in
effect.  In the event JAMS is unable or unwilling to conduct such arbitration,
or has discontinued its business, the parties agree that a representative
member, selected by the mutual agreement of the parties, of the American
Arbitration Association, San Francisco, California ("AAA"), shall conduct such
binding arbitration in accordance with the rules and procedures of the AAA then
in effect.  Notice of the demand for arbitration shall be filed in writing with
the other party to this Agreement and with JAMS (or AAA, if necessary).  In no
event shall the demand for arbitration be made after the date when institution
of legal or equitable proceedings based on such claim, dispute or other matter
in question would be barred by the applicable statute of limitations.  Any award
rendered by JAMS or AAA shall be final and binding upon the parties, and as
applicable, their respective heirs, beneficiaries, legal representatives,
agents, successors and assigns, and may be entered in any court having
jurisdiction thereof.  The obligation of the parties to arbitrate pursuant to
this clause shall be specifically enforceable in accordance with, and shall be
conducted consistently with, the provisions of Title 9 of Part 3 of the
California Code of Civil Procedure.  Any arbitration hereunder shall be
conducted in Palo Alto, California, unless otherwise agreed to by the parties.

     20.  Attorneys' Fees and Costs.  In the event of litigation, arbitration or
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any other action or proceeding between the parties to interpret or enforce this
Agreement or any part thereof or otherwise arising out of or relating to this
Agreement, the prevailing party shall be entitled to recover its costs related
to any such action or proceeding and its reasonable fees of attorneys,
accountants and expert witnesses incurred by such party in connection with any
such action or proceeding.  The prevailing party shall be deemed to be the party
which obtains substantially the relief sought by final resolution, compromise or
settlement, or as may otherwise be determined by order of a court of competent
jurisdiction in the event of litigation, an award or decision of one or more
arbitrators in the event of arbitration, or a decision of a comparable official
in the event of any other action or proceeding.  Every obligation to indemnify
under this Agreement includes the obligation to pay reasonable fees of
attorneys, accountants and expert witnesses incurred by the indemnified party in
connection with matters subject to indemnification.

     21.  Entire Agreement.  This Agreement supersedes any and all other
          ----------------                                              
agreements, either oral or in writing, between the parties with respect to the
employment of Employee by Employer and contains all of the covenants and
agreements between the parties with respect to

                                      -16-

 
the employment of Employee by Employer. Each party to this Agreement
acknowledges that no other representations, inducements, promises, or
agreements, oral or otherwise, have been made by any party, or anyone acting on
behalf of any party, which are not set forth herein, and that no other
agreement, statement, or promise not contained in this Agreement shall be valid
or binding on either party.

     22.  Modifications.  Any modification of this Agreement will be effective
          -------------                                                       
only if it is in writing and signed by a party or its authorized representative.

     23.  Waiver.  The failure of either party to insist on strict compliance
          ------                                                             
with any of the terms, provisions, covenants, or conditions of this Agreement by
the other party shall not be deemed a waiver of any term, provision, covenant,
or condition, individually or in the aggregate, unless such waiver is in
writing, nor shall any waiver or relinquishment of any right or power at any one
time or times be deemed a waiver or relinquishment of that right or power for
all or any other times.

     24.  Partial Invalidity.  If any provision in this Agreement is held by a
          ------------------                                                  
court of competent jurisdiction to be invalid, void, or unenforceable, the
remaining provisions shall nevertheless continue in full force and effect
without being impaired or invalidated in any way.

     25.  Interpretation.  This Agreement shall be construed without regard to
          --------------                                                      
the party responsible for the preparation of the Agreement and shall be deemed
to have been prepared jointly by the parties.  Any ambiguity or uncertainty
existing in this Agreement shall not be interpreted against either party, but
according to the application of other rules of contract interpretation, if an
ambiguity or uncertainty exists.

                                      -17-

 
     26.  Governing Law and Venue.  The laws of the State of California, other
          -----------------------                                             
than those laws denominated choice of law rules, shall govern the validity,
construction and effect of this Agreement.  Any action which in any way involves
the rights, duties and obligations of the parties hereunder shall be brought in
the courts of the State of California and venue for any action or proceeding
shall be in Santa Clara County or in the United States District Court for the
Northern District of California, and the parties hereby submit to the personal
jurisdiction of said courts.

     27.  Payments Due Deceased Employee.  If Employee dies prior to the
          ------------------------------                                
expiration of the term of his employment, any payments that may be due Employee
from Employer under this Agreement as of the date of death shall be paid to
Employee's executors, administrators, heirs, personal representatives,
successors, or assigns.

     IN WITNESS WHEREOF, the parties have executed this Agreement as of the date
set forth above.

EMPLOYER:                                   EMPLOYEE:

GREATER BAY BANCORP

By:  /s/ Duncan L. Matteson                 /s/ David L. Kalkbrenner
     ----------------------                 ------------------------
     Duncan L. Matteson                     David L. Kalkbrenner
     Co-Chairman of the Board

By:  /s/ John M. Gatto
     -----------------
     John M. Gatto
     Co-Chairman of the Board

                                      -18-