Exhibit 3.1

AMENDMENT TO FOURTH AMENDED AND RESTATED BYLAWS OF RESMED INC.

The FOURTH AMENDED AND RESTATED BYLAWS OF RESMED INC. are hereby amended as follows

1. Article 1 Section 9 is hereby amended in its entirety as follows:

Section 9. Voting.

Each director to be elected by the stockholders of the Company shall be elected by the affirmative vote of a majority of the votes cast with respect to such director by the shares represented and entitled to vote therefore at a meeting of the stockholders for the election of directors at which a quorum is present (an “Election Meeting”); provided, however, that if the Board determines that the number of nominees exceeds the number of directors to be elected at such meeting (a “Contested Election”), and the Board has not rescinded such determination by the record date of the Election Meeting as initially announced, each of the directors to be elected at the Election Meeting shall be elected by the affirmative vote of a plurality of the votes cast by the shares represented and entitled to vote at such meeting with respect to the election of such director.

For purposes of this Section 9, a “majority of the votes cast” means that the number of votes cast “for” a candidate for director or other action exceeds the number of votes cast “against” that candidate or other action (with “abstentions” and “broker non-votes” not counted as a vote cast either “for” or “against”). In an election other than a Contested Election, stockholders will be given the choice to cast votes “for” or “against” the election of directors or to “abstain” from such vote and shall not have the ability to cast any other vote with respect to such election of directors. In a Contested Election, stockholders will be given the choice to cast “for” or “withhold” votes for the election of directors and shall not have the ability to cast any other vote with respect to such election of directors. In the event an Election Meeting involves the election of directors by separate votes by class or classes or series, the determination as to whether an election constitutes a Contested Election shall be made on a class by class or series by series basis, as applicable.

Whenever any corporate action, other than the election of directors, is to be taken by vote of the stockholders at a meeting, it shall, except as otherwise required by law or the Certificate of Incorporation, be authorized by a majority of the votes cast thereat, in person or by proxy.

2. The effective date of this Amendment shall be November 17, 2011.

CERTIFICATE OF SECRETARY

I, the undersigned, do hereby certify:

(1) That I am the duly elected and acting Secretary of ResMed Inc., a Delaware corporation; and

(2) That the foregoing Amendment to the Fourth Amended and Restated Bylaws as duly approved and adopted by the Board of Directors on November 16, 2011, and together with the Fourth Amended and Restated Bylaws as filed with the SEC on December 14, 2007, as amended, constitute the duly authorized bylaws of the corporation.

IN WITNESS WHEREOF, I have hereunto subscribed my name this 22nd day of November, 2011.