Exhibit 3.1

CERTIFICATE OF AMENDMENT

OF THE RESTATED

CERTIFICATE OF INCORPORATION

OF

RESMED INC.,

a Delaware corporation

ResMed Inc., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (this “Corporation”), DOES HEREBY CERTIFY:

1. The name of the Corporation is ResMed Inc. The Corporation was originally incorporated under the name ResCare Medical Systems Ltd., and the original Certificate of Incorporation of the Corporation was filed with the Secretary of State of the State of Delaware on March 31, 1994.

2. That the Board of Directors of this Corporation, acting pursuant to the authority of Section 141(f) of the General Corporation Law of the State of Delaware, adopted a resolution setting forth a proposed amendment of the Certificate of Incorporation of this Corporation. The resolution setting forth the proposed amendment is as follows:

“NOW, THEREFORE, BE IT RESOLVED, that the Restated Certificate of Incorporation of this Corporation be amended by changing the first paragraph of Article Fourth thereof so that, as amended, the first paragraph of Article Fourth shall read in its entirety as follows:

“FOURTH: a) The Corporation shall be authorized to issue the following shares of Capital Stock:

3. This Amendment of the Restated Certificate of Incorporation was duly adopted by the holders of a majority of the issued and outstanding shares of the Common Stock of the Corporation, par value $0.004 per share, in accordance with the provisions of Sections 222 and 242 of the General Corporation Law of the State of Delaware.

IN WITNESS WHEREOF the undersigned has caused this Certificate of Amendment to be duly executed as of the 9th day of May, 2006.