<PAGE>

                                                             Exhibit 10.(i)(iii)



                                   AGREEMENT

  THIS AGREEMENT is made effective as of the 18th day of December 2000, by and
between Becton, Dickinson and Company (the "Company"), and John R. Considine,
(the "Considine").

                                 WITNESSETH:

  WHEREAS, Considine received an offer for the position Executive Vice
President, Chief Financial Officer for the Company pursuant to a letter (the
"Offer Letter") dated May 17, 2000 from Edward J. Ludwig, the Company's
President and Chief Executive Officer

  WHEREAS, the Offer Letter described certain terms and conditions of
Considine's employment for the Company, including his right to receive certain
post-retirement health care benefits under the Company's post-retirement health
care benefit program (the "Retiree Medical Plan");

  WHEREAS, on May 19, 2000, Considine accepted the offer contained in the Offer
Letter; and

  WHEREAS, Considine and the Company, by this Agreement, wish to clarify and
describe the Company's obligation (initially described in the Offer Letter) to
provide Considine with any post-retirement health care benefits.

  NOW, THEREFORE, in consideration of the mutual covenants and agreements
hereinafter set forth, and intending to be legally bound, the Company and
Considine agree as follows:

  1.    Retiree Medical Plan Eligibility:  This Agreement describes Considine's
eligibility for participation in the Retiree Medical Plan.  Except as otherwise
provided herein, all other terms, conditions, rights and obligations of
Considine and the Company with respect to the Retiree Medical Plan, including
(but not limited to) benefits and premium payments, shall be governed by the
terms of the Retiree Medical Plan.  Notwithstanding the foregoing, if the terms
of this Agreement conflict with the Retiree Medical Plan, this Agreement shall
be deemed to be an amendment to such Plan.  The following describes particular
rules regarding Considine's Retiree Medical Plan eligibility:

  a.  Termination of Employment On or After Age 55.  Upon Considine's
      --------------------------------------------
termination of employment for any reason on or after his attainment of age 55,
he shall be eligible to participate in the Retiree Medical Plan pursuant to the
terms, conditions, and limitations of such
<PAGE>

Plan in effect at such date, subject to Considine's payment of the applicable
premium for retiree medical coverage that otherwise applies to retired employees
of the Company.

  b.  Termination of Employment Before Age 55.
      ---------------------------------------

      (1)  Voluntary Termination or Termination for Cause Before Age 55.  If,
           ------------------------------------------------------------
prior to his attaining age 55, Considine voluntarily terminates his employment
or if Considine's employment is terminated by the Company "for cause" (as such
term is defined in Section 4(b) of the Change in Control Agreement entered into
between the Company and Considine), the Company shall have no obligation to
provide Considine with any retiree medical benefit coverage, whether under the
Retiree Medical Plan or otherwise.

      (2)  Mutual Agreement.  Notwithstanding the preceding paragraph (1), if
           ----------------
Considine's employment is terminated prior to his attaining age 55 and that
termination is at the mutual agreement of the Company and Considine, Considine
shall be entitled to participate in the Retiree Medical Plan upon his attainment
of age 55, pursuant to the terms, conditions, and limitations of such Plan in
effect at such date, subject to Considine's payment of the applicable premium
for retiree medical coverage that otherwise applies to retired employees of the
Company.

  c.  Death or Disability While Actively Employed.  Upon Considine's termination
      -------------------------------------------
of employment due  to his death or disability, Considine's eligibility for
benefits under the Retiree Medical Plan shall be unaffected by this Agreement
and he (or his surviving spouse) shall only be entitled to participate in the
Retiree Medical Plan (if at all) to the same extent as any other employee of the
Company who terminates employment due to death or disability at the same age as
Considine (at his death or disability) and with the same years of credited
service as Considine (at his death or disability).  Any Retiree Medical Plan
coverage under such conditions shall be provided pursuant to the terms,
conditions, and limitations of such Plan in effect at such date, subject to the
payment of the applicable premium for retiree medical coverage that otherwise
applies with respect to retired employees of the Company.

  d.  Change in Control.  If Considine's employment is terminated following a
      -----------------
Change in Control (as defined in the Change in Control Agreement between the
Company and Considine), Considine shall be eligible to participate in the
Retiree Medical Plan upon the later of his attainment of age 55 or the
exhaustion of medical coverage otherwise provided by the Company pursuant to the
terms of Considine's Change in Control Agreement.  Such coverage shall be
provided pursuant to the terms, conditions, and limitations of such Plan in
effect at such date, subject to the payment of the applicable premium for
retiree medical coverage that otherwise applies with respect to retired
employees of the Company.
<PAGE>

  2.    Non-Assignment:  Considine's right to the retiree medical benefits
described in this Agreement may not be assigned, transferred, pledged or
otherwise encumbered.

  3.  Tax Consequences: The Retiree Medical Plan is subject to certain federal
income tax rules that limit the extent to which tax-free coverage may be
provided on a discriminatory basis in favor of highly compensated individuals.
There can be no assurance that such coverage may continue to be provided to
Considine on a tax-favored basis if Considine's coverage under the Retiree
Medical Plan is made available to him at a time when it is not otherwise
available to any other terminated or retired employee of the Company.

  4.    No Employment Guarantee:  Nothing contained herein shall be construed as
conferring upon Considine the right to continue in the employ of the Company in
any capacity and no rights are acquired by the Retiree Medical Plan or the
Agreement except as expressly provided herein.

  5.    Plan Committee:  The senior human resources officer of the Company shall
have full power and authority to interpret, construe and administer this
Agreement and the Retiree Medical Plan, and such Committee's interpretations
hereof, and all actions hereunder, shall be binding and conclusive on all
persons and for all purposes. No member of the Compensation and Benefits
Committee of the Board or the senior human resources officer shall be liable to
any person for any action taken or omitted in connection with the interpretation
and administration of this Agreement unless attributable to such member's
willful misconduct.

  6.    Binding Effect:  This Agreement shall be binding upon and inure to the
benefit of the Company, its successors and assigns, and Considine, and
Considine's heirs, executors, administrators and legal representatives.

  7.    Controlling Law:  This Agreement shall be construed in accordance with
and governed by the laws of the State of New Jersey except to the extent
governed by applicable Federal law.

  8.    Termination or Amendment of Retiree Medical Plan:  Considine understands
and acknowledges that the Board of Directors of the Company or its delegate may
terminate or amend the Retiree Medical Plan at any time and for any reason.  In
the event of any such amendment, Considine shall be eligible for the same
coverage under the Retiree Medical Plan as all other similarly situated retired
employees of the Company otherwise entitled to coverage under the Retiree
Medical Plan.

  9.    Entire Agreement:  Except as expressly provided herein, this Agreement
and the underlying Retiree Medical Plan:  (i) supersede all other understandings
and agreements, oral or
<PAGE>

written, between the parties with respect to the subject matter of this
Agreement; and (ii) constitute the sole agreement between the parties with
respect to its subject matter. Each party acknowledges that: (i) no
representations, inducements, promises or agreements, oral or written, have been
made by any party or by anyone acting on behalf of any party, which are not
embodied in this Agreement; and (ii) no agreement, statement or promise not
contained in this Agreement shall be valid or binding on the parties unless such
change or modification is in writing and is signed by the parties.

  IN WITNESS WHEREOF, the parties have executed this Agreement signed this 18th
day of December, 2000 and effective as of the day and year first
above written.

                                  BECTON, DICKINSON AND COMPANY


                                  By:    /s/ Edward J. Ludwig
                                         _____________________________________
                                  Name:      Edward J. Ludwig
                                         _____________________________________
                                  Title: President and Chief Executive Officer
                                         _____________________________________

                                  JOHN R. CONSIDINE

                                  /s/ John R. Considine
                                  __________________________________