SIXTH AGREEMENT TO AMEND THE FLOATING RATE NOTE SUPPORT AGREEMENT

EXHIBIT 10.1

SIXTH AGREEMENT TO AMEND THE FLOATING RATE NOTE SUPPORT AGREEMENT

THIS SIXTH AMENDMENT is made as of this 22^nd day of February, 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 an Agreement to Amend the Floating Rate Note Support Agreement dated November 29, 2010, a Second Agreement to Amend the Floating Rate Note Support Agreement dated December 15, 2010, a Third Agreement to Amend the Floating Rate Note Support Agreement dated January 11, 2011, a Fourth Agreement to Amend the Floating Rate Note Support Agreement dated January 27, 2011 and a Fifth Agreement to Amend the Floating Rate Note Support Agreement dated February 7, 2011, the “Support Agreement”); and

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

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:

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

Each Consenting Noteholder party to this Sixth Amendment hereby represents and warrants, severally and not jointly, to each of the other parties to this Sixth Amendment (and acknowledges that each of the other parties to this Sixth 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 Sixth 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 Sixth Amendment.

The Support Agreement is hereby amended as follows:

- 2 -

“(i) any single transaction or series of related transactions that involves assets having a Fair Market Value of less than $1.0 million or (ii) any transaction described in a schedule to this Indenture, provided, however, that the transactions described in the foregoing clauses (i) and (ii) shall not be deemed an Asset Sale (and the Net Proceeds from such transactions not subject to Section 3.11 and Section 4.10 hereof) only to extent that the Net Proceeds resulting from such transactions are less than $10.0 million in the aggregate;”

“the license of any intellectual property of the Company or any of its Restricted Subsidiaries in the ordinary course of business that is not material to the Company or any of its Restricted Subsidiaries (as applicable), taken as a whole, up to an aggregate Fair Market Value of $5.0 million for all such transactions;”

“any single transaction or series of related transactions involving the sale of assets, where the Net Proceeds resulting from such transactions does not cause the Company and its Restricted Subsidiaries to have consummated Asset Sales, measured from the date hereof, not otherwise excluded by the exclusions in (1) through (10) above, resulting in aggregate Net Proceeds greater than $10.0 million (the “First Asset Sale Threshold”); provided, however, that, upon the aggregate Net Proceeds resulting from all such sales of assets, measured from the date hereof, exceeding the First Asset Sale Threshold, the amount of the aggregate Net Proceeds which is less than the First Asset Sale Threshold shall continue to be deemed not subject to Section 3.11 and Section 4.10 hereof;”

“Notwithstanding the foregoing, if at any time the LIBOR rate as so determined is less than 1.25%, the LIBOR rate shall be deemed to be 1.25%.”

- 3 -

“and includes any payment to former shareholders of Quill in respect of any sale of Quill related assets pursuant to a settlement agreement dated January 27, 2011.”

“Within 180 days after the receipt of any Net Proceeds from an Asset Sale, the Net Proceeds resulting from which causes the Company and its Restricted Subsidiaries to have consummated Asset Sales, measured from the date hereof, resulting in aggregate Net Proceeds less than $25.0 million (the “Second Asset Sale Threshold”), the Company (or the applicable Restricted Subsidiary, as the case may be) may apply such Net Proceeds at its option:

provided, however, that, in the event the Net Proceeds resulting from an Asset Sale causes the aggregate Net Proceeds for all Asset Sales by the Company and its Restricted Subsidiaries, measured from the date hereof, to exceed the Second Asset Sale Threshold, the amount of the aggregate Net Proceeds which is less than the Second Asset Sale Threshold shall continue to be subject to this paragraph.”

“Any Net Proceeds from (i) Asset Sales that are not applied or invested as provided in the second paragraph of this Section 4.10 or (ii) Asset Sales the Net Proceeds resulting from which cause the Company and its restricted Subsidiaries to have consummated Asset Sales, measured from the date hereof, resulting in Net Proceeds greater than the Second Asset Sale Threshold, where such Net Proceeds are not applied to repay Indebtedness and reduce commitments as contemplated by Subsection (1) in the second paragraph of this Section 4.10 (except for Net Proceeds subject to the fifth paragraph of this Section 4.10) will constitute “Excess Proceeds.” When the aggregate amount of Excess Proceeds exceeds $5.0

- 4 -

million, within 20 days thereof, the Company will make an Asset Sale Offer to all Holders of Notes and all holders of other Indebtedness that is pari passu with the Notes containing provisions similar to those set forth in this Indenture with respect to offers to purchase or redeem with the proceeds of sales of assets in accordance with Section 3.11 hereof to purchase the maximum principal amount of Notes and such other pari passu Indebtedness that may be purchased out of the Excess Proceeds. The offer price in any Asset Sale Offer will be equal to 100% of the principal amount plus accrued and unpaid interest, if any, to the date of purchase, and will be payable in cash. If any Excess Proceeds remain after consummation of an Asset Sale Offer, the Company may use those Excess Proceeds for any purpose not otherwise prohibited by this Indenture. If the aggregate principal amount of Notes and other pari passu Indebtedness tendered into such Asset Sale Offer exceeds the amount of Excess Proceeds, the Trustee will select the Notes and such other pari passu Indebtedness to be purchased on a pro rata basis. Upon completion of each Asset Sale Offer, the amount of Excess Proceeds will be reset at zero.”

“However, the consent of Holders of seventy-five percent (75%) in aggregate principal amount of the then outstanding Notes (including without limitation, Additional Notes, if any) voting as a single class (including, without limitation, consents obtained in connection with a tender offer or exchange offer for, or purchase of, the Notes) shall be required for any amendment, supplement or waiver under this Section 9.02 that amends, supplements, or waives the application of, as applicable, (i) the second subsection (1), subsection (6) or subsection (11) in the definition of “Asset Sale” in Section 1.01 hereof; (ii) the definition of “LIBOR” in Section 1.01 hereof; (iii) the definition of “Net Proceeds” in Section 1.01 hereof; (iv) the second, fourth or fifth paragraphs of Section 4.10 hereof; or (v) this paragraph.”

- 5 -

“not (A) object to, delay, impede or take any other action to interfere with the acceptance or implementation of the Exchange Transaction or the Recapitalization Transaction; (B) propose, file, support or vote in favour of any alternative exchange offer, restructuring, workout or plan of compromise or arrangement or reorganization of or for the Companies; or (C) take any action, directly or indirectly, that is materially inconsistent with, or is intended or is likely to interfere with the consummation of, the Exchange Transaction, except as required by applicable Law or by any stock exchange rules, by any other regulatory authority having jurisdiction over the Consenting Noteholder or by any court of competent jurisdiction.”

“Each Consenting Noteholder agrees to support the Recapitalization Transaction and execute a Waiver Letter in a form acceptable to the Trustee, pursuant to which the Consenting Noteholder agrees to waive any and all “Defaults” and “Events of Default” (as defined in the FRN Indenture), and change of control, if any, that may arise as a result of the steps to implement or completion of the Recapitalization Transaction pursuant to an exchange offer, plan of arrangement under the Canada Business Corporations Act (Canada) or any plan or proceedings under any insolvency proceeding or statute in Canada or the United States, including, without limitation, the Companies’ Creditors Arrangement Act, or the United States Bankruptcy Code, and, if applicable, waive any cross-default under the FRN Indenture that may arise as a result of Angiotech’s failure to pay any interest or principal or other payments that may be due and payable now or in the future under the Senior Subordinated Note Indenture and any event of default resulting from the filing by the Companies under the CCAA and Chapter 15 of the United States Bankruptcy Code (collectively, the “Waiver Matters”). For greater certainty, nothing in this Agreement requires the Consenting Noteholders or any of them to indemnify the Trustee or any other Person in any manner whatsoever. As an alternative to effecting the Exchange Terms by way of exchange offer, the Companies may complete the Exchange Transaction by way of (i) a plan under the Canada Business Corporations Act (Canada); (ii) any plan or proceedings under any insolvency proceeding or statute in Canada or the United States, including, without limitation, the Companies’ Creditors Arrangement Act, or the United States Bankruptcy Code; or (iii) a consent solicitation and amendment to the FRN Indenture (collectively, the “Alternative Transaction Structures”), and the Consenting Noteholder hereby consents to and agrees to vote in favour of the completion of the Exchange Transaction pursuant to any of the Alternative Transaction Structures, provided that the Consenting Noteholder receives Floating Rate Notes that have the attributes of the New Floating Rate Notes as described in Section 1 hereof. Without limiting the generality of the foregoing, provided that,

- 6 -

the Exchange Transaction results in the New Floating Rate Notes having the attributes described in the Exchange Offering Memorandum dated February 10, 2011, modified to reflect Subsection (1)(a) of this Agreement, subject to the rights of the Sixth Amendment Consenting Noteholders under the Fee Undertaking, all Consenting Noteholders shall support, consent to and not oppose the position of the Company on any motion or other proceeding in the Companies’ proceedings under the CCAA or Chapter 15 of the United States Bankruptcy Code or any other related proceeding, including the sanctioning of the Companies’ plan of arrangement to the extent the Company’s position is supported by Consenting Noteholders holding not less than a majority of the aggregate principal amount of Floating Rate Notes subject to this Agreement.”

“This 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 Floating Rate Notes subject to this Agreement; provided, however, that this Agreement may not be modified, amended or supplemented as to any of the Sixth Amendment Terms, and none of the Sixth Amendment Terms shall be waived, in each case, without the consent of the Consenting Noteholders holding not less than 75% of the aggregate principal amount of Floating Rate Notes subject to this Agreement.”

“Notwithstanding anything to the contrary in Section 15(n) hereof, if this Agreement is amended, modified or supplemented or any matter herein is approved, consented to or waived: (i) in a manner that materially adversely affects the consideration described in Section 1 hereof to be provided to Noteholders or (ii) such that the Outside Date is extended beyond October 15, 2011, then any Consenting Noteholder that objects to any such amendment, modification, supplement, approval, consent or waiver of this Agreement may terminate its obligations under this Agreement upon five (5) Business Days’ written notice to the other Parties hereto (each, an “Objecting Noteholder”) and shall thereupon no longer be a Consenting Noteholder; provided, further, that, in the event that the Fee Undertaking is breached by Angiotech, in each case, any of the Sixth Amendment Consenting Noteholders may terminate its obligations under this Agreement upon five (5) Business Days’ written notice to the other Parties hereto and shall thereupon be considered an Objecting Noteholder and no longer be a Consenting Noteholder and have all the rights it would have had as if it never became a party to this Agreement.”

“16. Releases

- 7 -

- 8 -

“Advisors” means Goodmans LLP, Houlihan Lokey, and Latham & Watkins LLP.

“Blackstone” means The Blackstone Group LP.

“CCAA” means the Companies’ Creditors Arrangement Act, R.S.C. 1985, c. C-36, as amended.

“CCAA Proceeding” means the proceeding commenced by the Companies under the CCAA on the Order Date in the Supreme Court of British Columbia at Vancouver under No. S110587.

“DIP Lender” shall have the meaning ascribed thereto in the Initial Order.

“DIP Credit Agreement” means the credit agreement dated February 7, 2011 between the Companies, as borrowers and guarantors, certain lenders signatory thereto and Wells Fargo, as arranger and administrative Agent.

- 9 -

“Fee Undertaking” means that certain undertaking dated as of the date of the Sixth Amendment executed by Angiotech in favour of the Sixth Amendment Consenting Noteholders.

“Initial Order” means the order obtained by the Companies (as may be amended, restated or varied from time to time) made by the Honourable Justice Walker of the Supreme Court of British Columbia under the CCAA dated January 28, 2011.

“Monitor” means Alvarez & Marsal Canada Inc., as Court-appointed Monitor in the CCAA Proceeding of the Companies.

“Order” means any order of the Court made in connection with the CCAA Proceeding of the Plan.

“Order Date” means January 28, 2011.

“Plan” means the Plan of Compromise or Arrangement filed by the Companies under the CCAA, as such Plan may be amended, supplemented or restated from time to time in accordance with the terms thereof.

“Released Party” shall have the meaning ascribed thereto in Section 16 of this Agreement.

“Sanction Order” means the Order of the Court sanctioning and approving the Plan.

“Sixth Amendment” means that certain amendment hereof dated as of February 22, 2011.

“Sixth Amendment Consenting Noteholders” means those holders of Floating Rate Notes that first executed a Consent Agreement as of the date of the Sixth Amendment.

“Sixth Amendment Terms” means the amendatory language in respect of the Support Agreement set forth in subsections (A) through and including (H) of section 3 of the Sixth Amendment.

“Subordinated Note Indenture Trustee” means U.S. Bank National Association in its capacity as indenture trustee under the Subordinated Note Indenture and any duly appointed successor indenture trustee thereunder.

“Wells Fargo” means Wells Fargo Capital Finance, LLC, in its capacity as agent and lender under the Wells Fargo Credit Agreement and DIP lender under the DIP Credit Agreement.

- 10 -

“Court” means the Ontario Superior Court of Justice or the Supreme Court of British Columbia.

“Wells Fargo Credit Agreement” means the Credit Agreement dated as of February 27, 2009, as amended, between the Companies, as borrowers and guarantors, the lenders signatory thereto and Wells Fargo, as arranger and administrative agent as amended from time to time.

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

[The remainder of this page is intentionally left blank]

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