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                                                                  EXHIBIT 10.b.4

                             EMPLOYMENT AGREEMENT


     EMPLOYMENT AGREEMENT (this "Agreement") dated as of May 29, 2001 among Bay
View Capital Corporation, a Delaware corporation having its principal place of
business at 1840 Gateway Drive, San Mateo, CA 94404 ("Bay View"), Bay View Bank,
N.A., a national banking association having its principal place of business at
1840 Gateway Drive, San Mateo, CA 94404 ("BVB"), and John W. Rose, an individual
residing at 511 Anderwood Drive, Hermitage, PA 16148 (the "Executive").

                                  WITNESSETH:
                                  ----------

     WHEREAS, BVB is a wholly owned subsidiary of Bay View;

     WHEREAS, Bay View and BVB (collectively, the "Employers") desire to employ
the Executive, and the Executive desires to be employed by the Employers, all in
accordance with the terms and subject to the conditions set forth herein; and

     WHEREAS, the parties are entering into this Agreement to set forth and
confirm their respective rights and obligations with respect to the Executive's
employment by the Employers;

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
herein contained, the parties hereto, intending to be legally bound hereby,
mutually agree as follows:

     1.  Employment and Term.
         -------------------

         (a)  Effective on the later of the date hereof or the date of receipt
of all approvals from applicable regulatory agencies (or the waiver thereof)
required for the Executive's assumption of the Position (as hereafter defined)
(the "Effective Date"), (i) Bay View shall employ the Executive, and the
Executive shall be employed by Bay View, as the Chief Financial Officer of Bay
View and (ii) BVB shall employ the Executive, and the Executive shall be
employed by BVB, as the Chief Financial Officer of BVB (with all such positions
described in clauses (i) and (ii) hereof being collectively referred to herein
as the "Position"), in accordance with the terms and subject to the conditions
set forth herein for a term (the "Term") that shall commence on the Effective
Date and, subject to paragraphs 1(b), 1(c), 1(d) and 1(e) hereof, shall continue
for a period of three years.  Bay View and BVB shall be jointly and severally
liable to the Executive with respect to (i) all liabilities of BVB to the
Executive hereunder and (ii) all liabilities of Bay View to the Executive
hereunder; provided, however, that Bay View shall not be responsible for any
liability of BVB to the Executive to the extent that such
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liability has been discharged by BVB, and BVB shall not be responsible for any
liability of Bay View to the Executive to the extent that such liability has
been discharged by Bay View.

         (b)  Unless written notice in accordance with this paragraph 1
terminating the Executive's employment hereunder is given by either of the
Employers or the Executive, on each day this Agreement is in effect, the Term
shall be automatically extended for one additional day so that at all times this
Agreement shall have a then current three-year Term.  Unless otherwise provided
herein or agreed by the parties hereto, all of the terms and conditions of this
Agreement shall continue in full force and effect throughout the Term and, with
respect to those terms and conditions that apply after the Term, after the Term.

         (c)  Notwithstanding paragraph 1(b) hereof, the Employers, by action of
their Boards of Directors (the "Boards") and effective as specified in a written
notice thereof to the Executive in accordance with the terms hereof, shall have
the right to terminate the Executive's employment hereunder at any time during
the Term hereof, for Cause (as defined herein) or other than for Cause or on
account of the Executive's death or Permanent Disability (as defined herein),
subject to the provisions of this paragraph 1.

              (i)  "Cause" shall mean (A) the Executive's willful and continued
failure substantially to perform his material duties with the Employers as set
forth in this Agreement, or the commission by the Executive of any activities
constituting a violation or breach under any material federal, state or local
law or regulation applicable to the activities of BVB or Bay View, in each case,
after notice thereof from the Employers to the Executive and a reasonable
opportunity for the Executive to cease such failure, breach or violation in all
material respects, (B) fraud, breach of fiduciary duty, dishonesty,
misappropriation or other intentional material damage to the property or
business of BVB or Bay View by the Executive, (C) the Executive's repeated
absences other than for physical or mental impairment or illness, (D) the
Executive's admission or conviction of, or plea of nolo contendere to, any
felony or any other crime referenced in Section 19 of the Federal Deposit
Insurance Act that, in the reasonable judgment of the Boards, adversely affects
BVB's or Bay View's reputation or the Executive's ability to carry out his
obligations under this Agreement or (E) the Executive's non-compliance with the
provisions of paragraph 2(b) hereof after notice thereof from the Employers to
the Executive and a reasonable opportunity for the Executive to cure such non-
compliance.  Notwithstanding the foregoing, the Employers may not terminate the
Executive's employment hereunder for Cause unless the Executive is given (A)
written notice, in accordance with the By-laws of the Employers, of a special
meeting of the Boards to consider the termination of the Executive's employment
hereunder for Cause and (B) the opportunity for the Executive to address such
special meeting.

                                      -2-
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              (ii) "Permanent Disability" shall mean a physical or mental
disability such that the Executive is substantially unable to perform those
duties that he would otherwise be expected to continue to perform and the
nonperformance of such duties has continued for a period of 240 consecutive
days, provided, however, that in order to terminate the Executive's employment
hereunder on account of Permanent Disability, the Employers must provide the
Executive with written notice of the Boards' good faith determination to
terminate the Executive's employment hereunder for reason of Permanent
Disability not less than 30 days prior to such termination, which notice shall
specify the date of termination. Until the specified effective date of
termination by reason of Permanent Disability, the Executive shall continue to
receive compensation at the rates set forth in paragraph 3 hereof. No
termination of the Executive's employment hereunder because of Permanent
Disability shall impair any rights of the Executive under any disability
insurance policy maintained by the Employers at the commencement of the
aforesaid 240-day period.

         (d)  The Executive shall have the right to terminate his employment
hereunder at any time during the Term hereof for Good Reason or in the event a
Change in Control occurs.  As used herein:

              (i)  "Good Reason" shall mean (A) the Executive's Position or the
scope of the Executive's authority, duties or responsibilities as described in
this Agreement are materially diminished without the Executive's written
consent, excluding for this purpose any action not taken by the Employers in bad
faith and that is remedied by the Employers promptly following written notice
thereof from the Executive to the Employers; (B) a material breach by either
Employer of its respective obligations to the Executive under this Agreement,
which breach is not cured in all material respects to the reasonable
satisfaction of the Executive within 30 days (except in the case of a payment
default for which the cure period shall be 10 days), in each case following
written notice thereof from the Executive to the Employers or (C) any
termination of the Executive's employment hereunder without Cause; and

              (ii) "Change of Control" shall mean (A) the acquisition of shares
of Bay View by any "person" or "group" (as such terms are used in Rule 13d-3
under the Securities Exchange Act of 1934 as now or hereafter amended) in a
transaction or series of transactions that result in such person or group
directly or indirectly first owning beneficially more than 25% of Bay View's
Common Stock after the date of this Agreement, (B) the consummation of a merger
or other business combination after which the holders of voting capital stock of
Bay View do not collectively own 60% or more of the voting capital stock of the
entity surviving such merger or other business combination or the sale, lease,
exchange or other transfer in a transaction or series of transactions of all or
substantially all of the assets of BVB, but excluding therefrom the sale and
reinvestment of BVB's investment portfolio or (C) as the result of or in
connection with any cash tender offer or exchange offer, merger or other
business

                                      -3-
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combination, sale of assets or contested election of directors or any
combination of the foregoing transactions (a "Transaction"), the persons who
constituted a majority of the members of the Boards on the Effective Date and
persons whose election as members of the Boards was approved by such members
then still in office or whose election was previously so approved after the
Effective Date, but before the event that constitutes a Change of Control, no
longer constitute such a majority of the members of the Boards then in office.
A Transaction constituting a Change in Control shall only be deemed to have
occurred upon the closing of the Transaction.

         (e)  (i)  If (A) the Employers terminate the Executive's employment
hereunder for any reason other than for Cause and such termination occurs as of
a date that is within 270 days preceding or within 180 days after the
consummation of a Change in Control (such 270-day period and such 180-day period
being hereinafter collectively referred to as a "Change in Control Period"), (B)
this Agreement is terminated as a result of the death or Permanent Disability of
the Executive effective as of a date within a Change of Control Period, (C) the
Executive terminates his employment hereunder for Good Reason effective as of a
date within a Change in Control Period or (D) the Executive terminates his
employment hereunder within 180 days after the consummation of a Change in
Control, the Employers shall pay to the Executive or his estate promptly after
the event giving rise to such payment occurs an amount equal to the sum of (x)
(1) the Executive's Base Salary (as defined herein) accrued through the date the
termination of the Executive's employment hereunder is effective, (2) any Bonus
(as defined herein) required to be paid to the Executive pursuant to paragraph
3(b) hereof and (3) any amount in respect of excise taxes required to be paid to
the Executive pursuant to paragraph 1(f) hereof, with such payments, rights and
benefits described in clauses (x)(1), (x)(2) and (x)(3) hereof being
collectively referred to herein as the "Accrued Obligations," (y) an amount
equal to the aggregate premiums that would be payable by the Executive to
maintain in effect throughout the period (the "Subsequent Period") from the date
of the Executive's termination through the remainder of the Term had the
Executive remained employed (assuming no increase in insurance premium rates)
the same medical, health, disability and life insurance coverage provided to the
Executive by the Employers immediately prior to the date of such termination
(the "Benefit Obligations") and (z) a severance payment equal to 2.99 times the
sum of (1) the Executive's annual Base Salary as of the effective date of
termination of the Executive's employment hereunder and (2) the Bonus payable to
the Executive pursuant to paragraph 3(b) hereof for the year in which such
termination is effective.

              (ii) If (A) the Employers terminate the Executive's employment
hereunder for any reason other than for Cause effective as of a date that is not
within a Change in Control Period or (B) the Executive terminates his employment
hereunder for Good Reason effective as of a date that is not within a Change in
Control Period, the Employers shall pay the Executive, provided the Executive
concurrently signs and

                                      -4-
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delivers a general release in a form mutually acceptable to the Employers and
the Executive, an amount equal to the sum of (w) the Accrued Obligations, (x)
the Benefit Obligations and (y) the amount of Base Salary the Executive would
have received had he remained employed hereunder during the Subsequent Period.

              (iii)  If (A) the Employers terminate the Executive's employment
hereunder for Cause, (B) the Executive terminates his employment hereunder for
any reason other than Good Reason, his death or Permanent Disability or (C) this
Agreement is terminated by the Employers as a result of the death or Permanent
Disability of the Executive effective as of a date that is not within a Change
in Control Period, the sole obligation of the Employers shall be to pay the
Accrued Obligations to the Executive.

              (iv) Notwithstanding anything to the contrary contained in this
Agreement, the Employers shall have the right, upon prior written notice
delivered to the Executive on or prior to August 27, 2002, to terminate
Executive's employment without Cause effective as of September 27, 2002.  In the
event of a termination under this Section 1(e)(iv), the Employers shall pay the
Executive, provided the Executive concurrently signs and delivers a general
release in a form mutually acceptable to the Employers and the Executive, an
amount equal to the sum of (w) the Accrued Obligations, (x) an amount equal to
the aggregate premiums that would be payable by the Executive to maintain in
effect throughout the period (the "Calculation Period") from the date of the
Executive's termination through March 26, 2004 had the Executive remained
employed (assuming no increase in insurance premium rates) the same medical,
health, disability and life insurance coverage provided to the Executive by the
Employers immediately prior to the date of such termination, (y) the amount of
Base Salary the Executive would have received had he remained employed hereunder
during the Calculation Period and (z) the Bonus payable to the Executive
pursuant to paragraph 3(b) hereof for the year in which such termination is
effective.

         (f)  In the event that the independent public accountants of either of
the Employers or the Internal Revenue Service determines that any payment,
coverage or benefit provided to the Executive pursuant hereto is subject to the
excise tax imposed by Section 4999 of the Internal Revenue Code of 1986, as
amended (the "Code") or any successor provision thereof or any interest or
penalties incurred by the Executive with respect to such excise tax (such excise
tax, together with any such interest and penalties, are hereinafter collectively
referred to as the "Excise Tax"), the Employers, within 30 days thereafter,
shall pay to the Executive, in addition to any other payment, coverage or
benefit due and owing hereunder, an amount determined by multiplying the rate of
Excise Tax then imposed by Section 4999 by the amount of the "excess parachute
payment" received by the Executive, determined without regard to any payments
made to the Executive pursuant to this paragraph 1(f), and dividing the product
so obtained by the amount obtained by subtracting the aggregate local, state and
federal income

                                      -5-
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and FICA and health insurance taxes applicable to the receipt by the Executive
of the "excess parachute payment" and taking into account the deductibility for
federal income tax purposes of the payment of state and local income taxes
thereon (as affected by those provisions of the Code that act to reduce the
deductibility of itemized deductions), from the amount obtained by subtracting
from 1.00 the rate of Excise Tax then imposed by Section 4999 of the Code, it
being the intention of the parties hereto that the Executive's net after tax
position (after taking into account any interest or penalties imposed with
respect to such taxes) upon the receipt of the payments provided for by this
Agreement be no less advantageous to the Executive than the net after tax
position to the Executive that would have been obtained had Sections 280G and
4999 of the Code not been applicable to such payments. Except as otherwise
provided herein, all determinations to be made under this paragraph 1(f) shall
be made by tax counsel whose selection shall be reasonably acceptable to the
Executive and the Employers and whose fees and costs shall be paid for by the
Employers.

         (g)  Any notice of termination of this Agreement by the Employers to
the Executive or by the Executive to the Employers shall be given in accordance
with the provisions of paragraph 10 hereof.

         (h)  The Employers agree to reimburse the Executive for the reasonable
fees and expenses of the Executive's attorneys and for court and related costs
in any proceeding to enforce the provisions of this Agreement in which the
Executive is successful on the merits.

     2.  Duties of the Executive.
         -----------------------

         (a)  Subject to the ultimate control and discretion of the Boards of
the Employers, the Executive shall serve in the Position and perform all duties
and services commensurate with the Position.  Throughout the Term, the Executive
shall perform all duties reasonably assigned or delegated to him under the By-
laws of BVB and Bay View or from time to time by the Boards or the Chief
Executive Officers of the Employers consistent with the Position.  Except for
travel normally incidental and reasonably necessary to the business of BVB and
Bay View and the duties of the Executive hereunder, the duties of the Executive
shall be performed in the greater San Francisco, California metropolitan area.

         (b)  The Executive shall devote substantially all of the Executive's
business time and attention to the performance of the Executive's duties
hereunder and, during the term of his employment hereunder, the Executive shall
not engage in any other business enterprise that requires any significant amount
of the Executive's personal time or attention, unless granted the prior
permission of the Boards.  The foregoing provision shall not prevent the
Executive's purchase, ownership or sale of any interest in, or the Executive's
engaging (but not to exceed an average of five hours

                                      -6-
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per week) in, any business that does not compete with the business of BVB or Bay
View or the Executive's involvement in charitable or community activities,
provided, that the time and attention that the Executive devotes to such
business and charitable or community activities does not materially interfere
with the performance of his duties hereunder and that a material portion of the
time devoted by the Executive to charitable or community activities are devoted
to charitable or community activities within BVB's market area and further
provided that such conduct complies in all material respects with applicable
policies of BVB and Bay View.

         (c)  The Executive shall be entitled to 30 days of vacation leave
during each calendar year with full compensation, and to be taken at such time
or times, as the Executive and BVB shall mutually determine.  Earned but unused
vacation shall be accrued in accordance with Bay View's vacation policy.

     3.  Compensation.  For all services to be rendered by the Executive
         ------------
hereunder:

         (a)  Base Salary.  The Employers shall pay the Executive a base salary
              -----------
(the "Base Salary") at an annual rate of Two Hundred Forty Thousand Dollars
($240,000), plus such other compensation as may, from time to time, be
determined by the Employers.  At the end of each fiscal year of the Employers,
the Employers shall review the amount of the Executive's Base Salary, and shall
increase such Base Salary for the following year to such amount as the Boards
may determine in their discretion.  Such Base Salary and other compensation
shall be payable in accordance with the Employers' normal payroll practices as
in effect from time to time.

         (b)  Annual Bonus.  The Employers agree that the Executive shall
              ------------
receive, in accordance in all material respects with applicable policies of Bay
View relating to incentive compensation for executive officers, an annual bonus
(the "Bonus") payable in cash, at the same time as bonuses are paid to other
executive officers of the Employers, in such amount as may be fixed by the
Boards in their discretion based upon the performance of BVB and Bay View and
the contributions of the Executive to such performance, provided, however, that
the Executive shall receive a Bonus of not less than $120,000 in respect of the
services to be rendered by the Executive during the first year of the Term.

         (c)  Stock Options.  Subject to any required stockholder approval, Bay
              -------------
View hereby grants the Executive options (the "Options"), which shall be non-
qualified stock options, to purchase an aggregate of 150,000 shares of Bay
View's Common Stock at a price per share equal to the lesser of (i) the tangible
book value per share of Bay View's Common Stock as of March 31, 2001 or (ii) 85%
of the closing price of Bay View's Common Stock on the New York Stock Exchange
on the day before the day on which the prospectus supplement relating to an
offering by Bay View of certain transferable

                                      -7-
<PAGE>

rights permitting the holders of the rights to subscribe for and purchase
additional shares of Common Stock becomes effective (the "Exercise Price"). The
Options shall have the following other principal terms:

              (i)  the Options shall become exercisable and be vested, and
remain exercisable and vested for a term of five years from and after the
Effective Date, in three cumulative installments as follows:

                   (A) the first installment, consisting of 50,000 shares of
Bay View's Common Stock, shall become exercisable from and after the Effective
Date;

                   (B) the second installment, consisting of 50,000 shares of
Bay View's Common Stock, shall become exercisable from and after the first
anniversary of the Effective Date; and

                   (C) the third installment, consisting of 50,000 shares of
Bay View's Common Stock, shall become exercisable from and after the second
anniversary of the Effective Date;

              (ii) the Options shall become immediately exercisable and shall
remain exercisable for the remainder of their term in the event of (A) a Change
in Control, (B) a termination of this Agreement by the Employers without Cause
or (C) a termination of this Agreement by the Executive for Good Reason;

              (iii)  the Options shall terminate immediately in the event of (A)
a termination of this Agreement by the Employers for Cause or (B) a termination
of this Agreement by the Executive without Good Reason;

              (iv)  the Options shall remain exercisable until the earlier of
the expiration of their term or three years after the termination of this
Agreement by the Employers because of the Executive's death or Permanent
Disability and the Options shall become immediately exercisable if such
termination occurs during the 270 days preceding consummation of a Change in
Control;

              (v)  the Options are transferable by gift to members of the
Executive's family or to entities controlled by such family members or by will
or by the laws of descent and distribution;

              (vi)  in the event that the outstanding shares of Common Stock
subject to the Options are hereafter increased or decreased or changed into or
exchanged for a different number or kind of shares of Bay View or other
securities of Bay View or of another corporation by reason of a reorganization,
merger, consolidation, reclassification, stock split, reverse stock split, stock
dividend or

                                      -8-
<PAGE>

combination of shares of Common Stock, the Board of Directors of Bay View shall
make an appropriate and equitable adjustment in the number and kind of shares as
to which the Options or portion thereof then unexercised shall be exercisable
and in the Exercise Price. Such adjustment in the Options shall be made without
any change in the total price applicable to the unexercised portion of the
Options, except for any change in the aggregate price resulting from rounding-
off of share amounts or prices, and with any necessary corresponding adjustment
in the Exercise Price. In the event that Bay View from time to time hereafter
issues its Common Stock at a price less than the then prevailing market price on
the New York Stock Exchange on the date of any such issuance (the "Prevailing
Market Price"), the Board of Directors shall reduce the Exercise Price of that
portion of the Options not then exercised to the price determined by multiplying
the Exercise Price as then in effect by a fraction the numerator of which shall
be that price per share at which Bay View issued its Common Stock at a price
less than the Prevailing Market Price and the denominator of which shall be such
Prevailing Market Price. Any such adjustment made by the Board of Directors
shall be final and binding upon the Executive, Bay View and their respective
successors in interest;

              (vii)  if Bay View adopts an option plan for its employees that
provides for terms more favorable to the optionees thereunder than the terms of
the Options to the Executive, then, in such event, the terms of the Options
shall be amended so that the terms thereof incorporate such more favorable terms
of such option plan; and

              (viii)  subject to any required stockholder approval, Bay View
shall promptly file a Form S-8 registration statement with respect to the
Options with the Securities and Exchange Commission and shall use its best
efforts to cause such registration statement to remain effective for as long as
any of the Options remain exercisable.

         (d)  Other Benefits.  From and after the date hereof and throughout the
              --------------
Term:

              (i)  The Employers shall provide the Executive with an automobile
at the Employers' sole cost and expense. Such automobile shall be owned or
leased by Bay View or BVB. The Employers shall bear all gas, insurance, repairs,
maintenance, car telephone and other operating expenses for the automobile.

              (ii)  In connection with his relocation to the greater San
Francisco area, the Executive shall be entitled to receive: (A) reimbursement of
all reasonable expenses incurred by the Executive in establishing a residence in
the San Francisco, California area, including, without limitation, travel,
moving and relocation expenses, (B) reimbursement of the cost of round-trip
first-class or business-class airfares for "house-hunting" trips for Executive's
spouse and (C) $4,000 per month for temporary

                                      -9-
<PAGE>

housing in the greater San Francisco area until the earlier to occur of twelve
months from the Effective Date or the date on which the Executive takes
possession of a purchased residence in the greater San Francisco area; provided,
however, that upon expiration of such twelve-month period, the Compensation
Committee of Bay View shall consider an extension of the temporary housing
allowance if so requested by the Executive.

              (iii)  The Employers shall reimburse the Executive for the cost of
not more than two round-trip first-class or business-class airfares per month
for the Executive or Executive's spouse from San Francisco, California to
destinations in the eastern half of the United States.

              (iv)  The compensation provided for in this paragraph 3 shall be
in addition to such rights as the Executive may have, during the Executive's
employment hereunder or thereafter, to participate in and receive benefits from
or under any benefit plans the Employers may in their discretion establish for
their employees or executives. To the extent any of such benefits are taxable to
the Executive, the Executive shall be solely responsible for such taxes.

     4.  Expenses.  The Employers shall promptly reimburse the Executive for (a)
         --------
all reasonable expenses paid or incurred by the Executive in connection with the
performance of the Executive's duties and responsibilities hereunder, upon
presentation of expense vouchers or other appropriate documentation therefor,
(b) all reasonable professional expenses, such as licenses and dues and
professional educational expenses, paid or incurred by the Executive during the
Term and (c) the costs of a personal computer, cellular telephone and fax
machine for the Executive's residence in the San Francisco, California area,
including the monthly fees related to such devices.

     5.  Indemnification.  Notwithstanding anything in the Employers'
         ---------------
certificate of incorporation or their By-laws to the contrary, the Executive
shall at all times during his employment by the Employers, and thereafter, be
indemnified by the Employers to the fullest extent permitted by applicable law
for any matter in any way relating to the Executive's affiliation with the
Employers and/or its subsidiaries; provided, however, that if the Executive's
employment shall have been terminated by the Employers for Cause, then the
Employers shall have no obligation whatsoever to indemnify the Executive for any
claim arising out of the matter for which his employment shall have been
terminated for Cause or for any conduct of the Executive not within the scope of
the Executive's duties under this Agreement.

     6.  Confidential Information.  The Executive understands that in the course
         ------------------------
of his employment by the Employers the Executive will receive confidential
information concerning the business of the Employers and that the Employers
desire to protect.  The Executive agrees that he will not at any time during or
after the period of his

                                      -10-
<PAGE>

employment by the Employers reveal to anyone outside BVB or Bay View, or use for
his own benefit, any such information that has been designated as confidential
by the Employers or understood by the Executive to be confidential without
specific written authorization by the Employers. Upon termination of this
Agreement, and upon the request of the Employers, the Executive shall promptly
deliver to the Employers any and all written materials, records and documents,
including all copies thereof, made by the Executive or coming into his
possession during the Term and retained by the Executive containing or
concerning confidential information of the Employers and all other written
materials furnished to and retained by the Executive by the Employers for his
use during the Term, including all copies thereof, whether of a confidential
nature or otherwise.

     7.  Representation and Warranty of the Executive.  The Executive represents
         --------------------------------------------
and warrants that he is not under any obligation, contractual or otherwise, to
any other firm or corporation, which would prevent his entry into the employ of
the Employers or his performance of the terms of this Agreement.

     8.  Entire Agreement; Amendment.  This Agreement contains the entire
         ---------------------------
agreement between the Employers and the Executive with respect to the subject
matter hereof, and may not be amended, waived, changed, modified or discharged
except by an instrument in writing executed by the parties hereto.

     9.  Assignability.  The services of the Executive hereunder are personal in
         -------------
nature, and neither this Agreement nor the rights or obligations of the
Employers hereunder may be assigned by the Employers, whether by operation of
law or otherwise, without the Executive's prior written consent.  This Agreement
shall be binding upon, and inure to the benefit of, the Employers and their
permitted successors and assigns hereunder.  This Agreement shall not be
assignable by the Executive, but shall inure to the benefit of the Executive's
heirs, executors, administrators and legal representatives.

     10.  Notice.  Any notice that may be given hereunder shall be in writing
          ------
and be deemed given when hand delivered and acknowledged or, if mailed, one day
after mailing by registered or certified mail, return receipt requested, or if
delivered by an overnight delivery service, one day after the notice is
delivered to such service, to either party hereto at their respective addresses
stated above, or at such other address as either party may by similar notice
designate.  Copies of such notices also shall be sent to the Employers
attention: General Counsel, 1840 Gateway Drive, San Mateo, California 94404 and
to the Executive's counsel, attention:  Frederick W. Dreher, Esq., Duane, Morris
& Heckscher LLP, 4200 One Liberty Place, Philadelphia, Pennsylvania 19103-7396.

                                      -11-
<PAGE>

     11.  Specific Performance.  The parties agree that irreparable damage would
          --------------------
occur in the event that any of the provisions of paragraph 6 hereof were not
performed in accordance with their specific terms or were otherwise breached.
It is accordingly agreed that the parties shall be entitled to an injunction or
injunctions to prevent breaches of paragraph 6 hereof and to enforce
specifically the terms and provisions of paragraph 6 hereof, this being in
addition to any other remedy to which any party is entitled at law or in equity.

     12.  No Third Party Beneficiaries.  Nothing in this Agreement, express or
          ----------------------------
implied, is intended to confer upon any person or entity other than the parties
(and the Executive's heirs, executors, administrators and legal representatives
and the permitted transferees of the Options) any rights or remedies of any
nature under or by reason of this Agreement.

     13.  Successor Liability.  The Employers shall require any subsequent
          -------------------
successor, whether direct or indirect, by purchase, merger, consolidation or
otherwise, to all or substantially all of the business or assets of the
Employers to assume expressly and agree to perform this Agreement in the same
manner and to the same extent that the Employers would be required to perform it
if no such succession had taken place.

     14.  Mitigation.  The Executive shall not be required to mitigate the
          ----------
amount of any payment provided for in this Agreement by seeking other employment
or otherwise, nor shall the amount of any payment or benefit provided for in
this Agreement be reduced by any compensation earned by the Executive as the
result of employment by another employer or by retirement benefits payable after
the termination of this Agreement, except that the Employers shall not be
required to provide the Executive and his eligible dependents with medical
insurance coverage as long as the Executive and his eligible dependents are
receiving comparable medical insurance coverage from another employer.

     15.  Arbitration.  Any dispute that may arise between the parties hereto,
          -----------
including, without limitation, any dispute arising out of or relating to this
Agreement, shall be submitted to binding arbitration in accordance with the
Rules of the American Arbitration Association, except for any dispute excluded
from arbitration by law; provided that any such dispute shall first be submitted
to the Boards in an effort to resolve such dispute without resort to
arbitration, and provided, further, that the Boards shall have a period of 60
days within which to respond to the Executive's submitted dispute, and if the
Boards fail to respond within said time, or the Executive's dispute is not
resolved, the matter shall then be submitted for arbitration.  The results of
any arbitration pursuant to this Agreement shall be final and binding on the
parties hereto.

                                      -12-
<PAGE>

     16.  Waiver of Breach.  The failure at any time to enforce or exercise any
          ----------------
right under any of the provisions of this Agreement or to require at any time
performance by the other parties of any of the provisions hereof shall in no way
be construed to be a waiver of such provisions or to affect either the validity
of this Agreement or any part hereof, or the right of any party hereafter to
enforce or exercise its rights under each and every provision in accordance with
the terms of this Agreement.

     17.  No Attachment.  Except as required by law, no right to receive
          -------------
payments under this Agreement shall be subject to anticipation, commutation,
alienation, sale, assignment, encumbrance, charge, pledge or hypothecation or to
execution, attachment, levy or similar process or assignment by operation of
law, and any attempt, voluntary or involuntary, to effect any such action shall
be null, void and of no effect; provided, however, that nothing in this
paragraph 17 shall preclude the assumption of such rights by executors,
administrators or other legal representatives of the Executive or his estate and
their assigning any rights hereunder to the person or persons entitled hereto.

     18.  Severability.  The invalidity or unenforceability of any term, phrase,
          ------------
clause, paragraph, restriction, covenant, agreement or other provision hereof
shall in no way affect the validity or enforceability of any other provision, or
any part thereof, but this Agreement shall be construed as if such invalid or
unenforceable term, phrase, clause, paragraph, restriction, covenant, agreement
or other provision had never been contained herein unless the deletion of such
term, phrase, clause, paragraph, restriction, covenant, agreement or other
provision would result in such a material change as to cause the covenants and
agreements contained herein to be unreasonable or would materially and adversely
frustrate the objectives of the parties as expressed in this Agreement.

     19.  Survival of Benefits.  Any provision of this Agreement that provides a
          --------------------
benefit to the Executive and that by the express terms hereof does not terminate
upon the expiration of the Term shall survive the expiration of the Term and
shall remain binding upon the Employers until such time as such benefits are
paid in full to the Executive or his estate.

     20.  Construction.  This Agreement shall be governed by and construed in
          ------------
accordance with the internal laws of the State of California, without giving
effect to principles of conflict of laws.  All headings in this Agreement have
been inserted solely for convenience of reference only, are not to be considered
a part of this Agreement and shall not affect the interpretation of any of the
provisions of this Agreement.

                                      -13-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date first written above.



                                BAY VIEW CAPITAL CORPORATION


                                By: /s/ Robert B. Goldstein
                                   ------------------------
                                   Name: Robert B. Goldstein
                                   Title: President and Chief
                                          Executive Officer


                                BAY VIEW BANK, N.A.


                                By: /s/ Robert B. Goldstein
                                   ------------------------
                                   Name: Robert B. Goldstein
                                   Title: President and Chief
                                          Executive Officer


                                /s/ John W. Rose
                                -----------------
                                John W. Rose

                                      -14-