<PAGE>

                                                           Exhibit 10.10(b)

                           AMENDMENT TO RABBI TRUST

          The Trust Agreement dated as of a August 16, 1996 by and between
Mallinckrodt Group Inc., a New York Corporation and Wachovia Bank of North
Carolina (the "Trust Agreement") is hereby amended, effective as of June 20,
2000, as set forth below.

          Capitalized terms used herein without definition shall have the
respective meanings set forth in the Trust Agreement.

          1.   Preamble.
               --------

          The first WHEREAS clause of the Trust Agreement is restated in its
entirety to read as follows:

               "WHEREAS, the Company has adopted the employee benefit plans and
     arrangements listed on Schedule I hereto (collectively, the "Plans"),
     copies of which are attached hereto as Appendix A, including, without
     limitation, the severance agreements between the Company and the employees
     of the Company listed on Schedule I (the "Severance Agreements" and
     together with the Corporate Staff Change in Control Severance Plan
     identified on Schedule I, the "Severance Programs")"

          2.   Section 1.  Establishment of Trust.
               ----------------------------------

          Section 1(f) is restated in its entirety to read as follows:

               "(f)  Immediately prior to or upon a Change in Control, the
     Company shall make an irrevocable contribution to the Trust in an amount in
     cash or other property (of the type specified in Section 5(a)) that is
     sufficient to pay each Participant (determined by allocations to separate
     accounts for each Participant) the accrued benefits (the "BENEFITS') to
     which such Participant and such Participant's spouse would be entitled
     under the Plans as of such date (which shall be deemed to include an amount
     necessary to fund the aggregate cash severance obligation for all employees
     covered by Severance Agreements and all Participants under the Corporate
     Staff Change in Control Severance Plan if such employees' and Participants'
     employment were terminated immediately following the Change in Control,
     other than as a result of a Nonqualifying Termination (as defined in the
     Severance Programs) (the "REQUIRED FUNDING AMOUNT"). Concurrently with the
     contribution of the Required Funding Amount, the Company shall also deposit
     $250,000 in cash to a separate account of the Trust (the "TRUSTEE EXPENSE
     ACCOUNT"), which account shall be used to reimburse the Trustee for its
     fees and reasonable expenses hereunder as provided in Section 9."

          3.   The validity, interpretation, and enforcement of this amendment
shall be governed by the law of the State of New York. The invalidity or
unenforceabililty of any provision of this amendment shall not affect the
validity or enforceabililty of any other provision of this amendment or of the
Trust Agreement, as amended hereby, which other provisions shall remain in full
force and effect. This amendment may be executed in two or more counterparts,
each of which shall be deemed to be an original and all of which together shall
constitute one and the same instrument.
<PAGE>

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


                                     MALLINCKRODT INC.

Date:      June 20, 2000             By: /s/ Bruce K. Crockett
     ---------------------               --------------------------------
                                         Name: Bruce K. Crockett
                                         Title: Vice President Human Resources



                                     WACHOVIA BANK OF NORTH CAROLINA,
                                     N.A.


Date:      June 20, 2000             By: /s/ Joe O. Long
     ---------------------               --------------------------------
                                         Name: Joe O. Long
                                         Title: Sr. Vice President/GE
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                                                                      Schedule I

                                                                   July 20, 2000

Severance Agreements (or any successor retention agreements) between the Company
and the following employees:

Abbett, Barbara
Baldessari, Keith
Chawla, Ashok
Collins, Michael
Crockett, Bruce
Fercho, Bradley
Given, Douglass
Greenspan, Ronald
Hesemann, John
Higgons, Richard
Holman, C. Ray
Keller, Roger
Kupferer, David
McKinney, Douglas
Milosovich, Michael
Mulholland, Daniel
Rocca, Michael
Shivley, R. Scott
Stone, William
Voltolina, Frank
Rizzi, Oscar
Olukotun, Oye
Forrest Whittaker


Puritan Bennett SERP and Makeup Plans

Mallinckrodt Supplemental Benefit Plans

Unfunded Deferred Payment Obligations for Harold Brinner

Unfunded Deferred Payment Obligations for Harold Thayer

Pilots Supplemental Pension Plan

Puritan Bennett Deferred Compensation Plan (including Burt Dole)

Puritan Bennett Directors Pension Plan

Premium payments under Mallinckrodt's executive life insurance program

Mallinckrodt Supplemental Retirement Plan (parts A and B)

Corporate staff Change-in-Control Plan
<PAGE>

Deferral election plan for non-employee directors

Mallinckrodt Director's Retirement Service Plan

Mallinckrodt Director Retirement Plan

All other unfunded nonqualified deferred compensation or deferred employee or
director severance or retirement payment obligations of Mallinckrodt Inc. or its
subsidiaries