AMENDMENT TO RIGHTS AGREEMENT

Exhibit 10.5

AMENDMENT TO RIGHTS AGREEMENT

This Amendment to Rights Agreement dated as of March 3, 2005 (this “Amendment”), between Closure Medical Corporation, a Delaware corporation (“Closure Medical”), and American Stock Transfer & Trust Company (the “Rights Agent”).

WITNESSETH:

WHEREAS, Closure Medical and the Rights Agent constitute all of the parties to that certain Rights Agreement, dated as of July 30, 2001 (the “Rights Agreement”), and desire to amend the Rights Agreement as set forth herein.

NOW, THEREFORE, in consideration of the premises and of the mutual covenants and agreements herein contained, and intending to be legally bound hereby, and pursuant to the Rights Agreement and in accordance with Section 26 thereof, the parties hereto do hereby agree as follows (capitalized terms used but not defined herein have the meanings ascribed to such terms in the Rights Agreement):

1. Amendments to the Rights Agreement. The Rights Agreement shall be amended as follows:

(a) Section 1(a) of the Rights Agreement is hereby amended to add the following sentence at the end thereof:

“Notwithstanding the foregoing, Johnson & Johnson and its Affiliates and Associates shall not be or become an “Acquiring Person”, either individually or collectively, as the result of (i) the announcement of the Merger, (ii) the execution of the Merger Agreement or (iii) the consummation of the transactions contemplated by the Agreement and Plan of Merger substantially in the form attached hereto as Exhibit D (the “Merger Agreement”).”

(b) The following definitions shall be added to Section 1 of the Rights Agreement and the remaining sections shall be renumbered accordingly:

“1(s) “Merger” shall have the meaning assigned to such term in the Merger Agreement.”

(c) Section 1(c) of the Rights Agreement is hereby amended to add the following sentence at the end thereof:

“Notwithstanding the foregoing, Johnson & Johnson and its Affiliates and Associates shall not be deemed either individually or collectively, the “Beneficial Owner” of, or be deemed to “beneficially own,” any securities of the Company as the result of the execution of, or the exercise of any of their rights under, the Stockholder Agreement dated as of March 3, 2005 among Johnson

& Johnson and the individuals and other parties listed on Schedule A attached hereto, substantially in the form attached hereto as Exhibit E.”

(d) New Exhibits D and E are hereby added to the Rights Agreement in the forms set forth as Exhibits A and B hereto, respectively.

(e) Section 3(a) of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Rights Agreement to the contrary, a Distribution Date shall not be deemed to have occurred as the result of (i) the announcement of the Merger, (ii) the execution of the Merger Agreement or (iii) the consummation of the Merger or of the other transactions contemplated by the Merger Agreement.”

(f) Section 7(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

Subject to subsection (e), the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein including, without limitation, the restrictions on exercisability set forth in Section 9(c), Section 11(a)(iii) and Section 23(a) hereof) in whole or in part at any time after the Distribution Date upon surrender of the Rights Certificate, with the form of election to purchase and the certificate on the reverse side thereof duly executed, to the Rights Agent at the principal office or offices of the Rights Agent designated for such purpose, together with payment of the aggregate Purchase Price (except as provided in Section 11(q) hereof) with respect to the total number of Preferred Share Fractions (or Common Shares, other securities, cash or other assets, as the case may be) as to which such surrendered Rights are then exercisable (except as provided in Section 11(q) hereof), at or prior to the earliest of (i) the close of business on July 30, 2011 (the “Final Expiration Date”), (ii) the consummation of a transaction contemplated by Section 13(d) hereof, (iii) the time at which the Rights are redeemed or terminated as provided in Section 23 hereof, or (iv) immediately prior to the Effective Time (as defined in the Merger Agreement) (the earlier of (i), (ii), (iii) and (iv) being herein referred to as the “Expiration Date”).

(g) The following shall be added to Section 13(b) as a new clause (iii):

(iii) “Notwithstanding the foregoing, Johnson & Johnson and its Affiliates and Associates shall not be or become a “Principal

Party,” either individually or collectively, as the result of (A) the announcement of the Merger, (B) the execution of the Merger Agreement or (C) the consummation of the Merger or of the other transactions contemplated by the Merger Agreement.”

(h) Section 24(b) of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Rights Agreement to the contrary, the Company shall not be obligated to provide any notice pursuant to this Section 24(b) as a result of (i) the announcement of the Merger, (ii) the execution of the Merger Agreement or (iii) the consummation of the Merger or of the other transactions contemplated by the Merger Agreement.”

2. Miscellaneous.

(a) The laws of the State of Delaware shall govern the validity, interpretation, construction, performance, and enforcement of this Agreement, excluding the choice of laws provisions of the State of Delaware.

(b) Except as modified herein, all other terms and provisions of the Rights Agreement (including the Exhibits thereto) are unchanged and remain in full force and effect.

(c) This Amendment may be executed in counterparts, each of which shall be deemed an original, but all of which taken together shall constitute one and the same instrument. This Amendment shall become effective when each party to this Amendment shall have received a counterpart hereof signed by the other party to this Amendment.

(d) This Amendment shall be binding upon any permitted assignee, transferee, successor or assign to any of the parties hereto.

(e) If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment, and the Rights Agreement, shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

(f) The officer of Closure Medical executing this Amendment on behalf of Closure Medical hereby certifies on behalf of the company that this Amendment complies with Section 26 of the Rights Agreement.

(g) In all respects not inconsistent with the terms and provisions of this Amendment, the Rights Agreement is hereby ratified, adopted, approved and confirmed. In executing and delivering this Amendment, the Rights Agent shall be entitled to all the privileges and immunities afforded to the Rights Agent under the terms and conditions of the Rights Agreement.

IN WITNESS WHEREOF, the parties have caused this Amendment to be duly executed by their duly authorized representatives as of the date first written above.