EXHIBIT 10.1

THIRD AGREEMENT TO AMEND THE RECAPITALIZATION SUPPORT AGREEMENT

THIS THIRD AMENDMENT is made as of this 11^th 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 Subordinated Notes, executed a Recapitalization Support Agreement dated as of October 29, 2010 concerning the principal aspects of a Recapitalization of the Companies (as amended by the First Amendment and the Second Amendment, the “Support Agreement”);

AND WHEREAS, pursuant to Section 16(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 aggregate principal amount of Subordinated Notes;

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

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

AND WHEREAS, the Companies and 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 the Third Amendment collectively hold and/or exercise investment discretion over not less than a majority of the aggregate principal amount of outstanding Subordinated 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 Subordinated Notes disclosed to Goodmans as of such date, or (ii) has the investment and voting discretion with respect to the principal amount of Subordinated Notes disclosed to Goodmans as of such date; (b) it has the power and authority to bind the beneficial owner(s) of such Subordinated Notes to the terms of this Third Amendment; and (c) it has authorized and instructed Goodmans to advise Angiotech, in writing, of the aggregate amount of Subordinated 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 as follows:

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.

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5. Miscellaneous

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