EXHIBIT 3.6 CERTIFICATE OF AMENDMENT OF THE RESTATED CERTIFICATE OF INCORPORATION OF CARDIOTHORACIC SYSTEMS, INC. CardioThoracic Systems, Inc., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware, DOES HEREBY CERTIFY: FIRST: The name of this corporation is CardioThoracic Systems, Inc. This corporation was originally incorporated under the same name, and the original Certificate of Incorporation was filed with the Secretary of State of the State of Delaware on February 20, 1996. SECOND: That at a meeting of the Board of Directors of CardioThoracic Systems, Inc., resolutions were duly adopted setting forth proposed amendments of the Restated Certificate of Incorporation of said corporation, declaring said amendments to be advisable and calling for the submission thereof to the stockholders of said corporation for adoption. The resolutions setting forth the proposed amendments are as follows: RESOLVED: That the first paragraph of Article IV of the Restated Certificate of Incorporation of this corporation be amended and restated to read in its entirety as follows: The Corporation is authorized to issue two classes of shares of stock to be designated, respectively, Common Stock, $0.001 par value, and Preferred Stock, $0.001 par value. The total number of shares that the Corporation is authorized to issue is 65,100,000 shares. The number of shares of Common Stock authorized is 60,000,000. The number of shares of Preferred authorized is 5,100,000. RESOLVED FURTHER: That Article X of the Restated Certificate of Incorporation of this corporation be amended and restated to read in its entirety as follows: 1. Number of Directors. The number of directors which constitutes the whole Board of Directors of the corporation shall be designated in the Bylaws of the corporation. The directors shall be divided into three classes with the term of office of the first class (Class I) to expire at the annual meeting of stockholders held in 1998; the term of office of the second class (Class II) to expire at the annual meeting of stockholders held in 1999; the term of office of the third class (Class III) to expire at the annual meeting of stockholders held in 2000; and thereafter for each such term to expire at each third succeeding annual meeting of stockholders after such election. 2. Election of Directors. Elections of directors need not be by written ballot unless the Bylaws of the corporation shall so provide. THIRD: That thereafter, pursuant to resolution of its Board of Directors, the approval of the stockholders of said corporation was duly obtained in accordance with Section 242 of the General Corporation Law of the state of Delaware at which time the necessary number of shares as required by statute were voted in favor of the amendment. FOURTH: That said amendment was duly adopted in accordance with the provisions of Section 242 of the General Corporation Law of the State of Delaware. IN WITNESS WHEREOF, CardioThoracic Systems, Inc. has caused this certificate to be signed by Richard M. Ferrari, its President, and J. Casey McGlynn, its Secretary, this 27th day of May, 1997. BY: /s/ RICHARD M. FERRARI -------------------------------- Richard M. Ferrari, President ATTEST: /s/ J. CASEY MCGLYNN --------------------------------- J. Casey McGlynn, Secretary