EXHIBIT 10.2

THIRD AGREEMENT TO AMEND THE FLOATING RATE NOTE SUPPORT AGREEMENT

THIS THIRD AMENDMENT is made as of this 11th day of January 2011.

WHEREAS, (a) Angiotech Pharmaceuticals, Inc. (“Angiotech”), (b) the entities listed in Schedule A (together with Angiotech, the “Companies” and each a “Company”), and (c) each of the other Consenting Noteholders party hereto, each Consenting Noteholder being a holder of and/or investment advisor or manager with investment discretion over Floating Rate Notes, executed a Floating Rate Note Support Agreement dated as of October 29, 2010 concerning the principal aspects of an Exchange of Floating Rate Notes (as amended by the First Amendment and the Second Amendment, the “Support Agreement”);

AND WHEREAS, pursuant to Section 15(n) of the Support Agreement, the Support Agreement may be modified, amended or supplemented as to any matter by an instrument in writing signed by the Companies and Consenting Noteholders that represent not less than a majority of the outstanding Floating Rate Notes;

AND WHEREAS, the Consenting Noteholders representing not less than a majority of the aggregate principal amount of outstanding Floating Rate Notes executed an Agreement to Amend the Floating Rate Note Support Agreement dated as of November 29, 2010 (the “First Amendment”);

AND WHEREAS, the Consenting Noteholders representing not less than a majority of the aggregate principal amount of outstanding Floating Rate Notes executed a Second Agreement to Amend the Floating Rate Note Support Agreement dated as of December 15, 2010 (the “Second Amendment”);

AND WHEREAS, the Consenting Noteholders party to this third amendment (the “Third Amendment”) wish to further amend the Support Agreement in the manner set out in this Third Amendment;

AND WHEREAS, the Consenting Noteholders party to this Third Amendment collectively hold and/or exercise investment discretion over not less than a majority of the Floating Rate Notes;

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the Companies and the Consenting Noteholders party hereto hereby agree as follows:

1. Capitalized Terms

Capitalized Terms that are used but not otherwise defined herein shall have the meanings ascribed thereto in the Support Agreement.

2. Consenting Noteholders Party to this Third Amendment

Each Consenting Noteholder party to this Third Amendment hereby represents and warrants, severally and not jointly, to each of the other parties to this Third Amendment (and acknowledges that each of the other parties to this Third Amendment is relying upon such representations and warranties) that as of the date hereof: (a) it either (i) is the sole legal and beneficial owner of the principal amount of Floating Rate Notes disclosed to Houlihan Lokey as of such date, or (ii) has the investment and voting discretion with respect to the principal amount of Floating Rate Notes disclosed to Houlihan Lokey as of such date; (b) it has the power and authority to bind the beneficial owner(s) of such Floating Rate Notes to the terms of this Third Amendment; and (c) it has authorized and instructed Houlihan Lokey to advise Angiotech, in writing, of the aggregate amount of Floating Rate Notes held by the Consenting Noteholders that are party to this Third Amendment.

3. Amendments to the Support Agreement

The Support Agreement is hereby amended by deleting the reference to “January 11, 2011” in Section 5(d) of the Support Agreement and replacing it with “January 28, 2011”.

4. Support Agreement to apply in full force and effect

Except as expressly modified by the terms of this Third Amendment, the terms and conditions of the Support Agreement shall continue to apply in full force and effect, unamended.

5. Miscellaneous

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This Third Amendment has been agreed and accepted on the date first written above.