SAN FRANCISCO  The alliance between Apple and Google, two Silicon Valley giants with a powerful common enemy in Microsoft, is now clearly fraying.

Apple announced on Monday that Eric E. Schmidt, Google’s chief executive, was stepping down from its board. The move comes as the Federal Trade Commission is looking into whether the two companies violated antitrust laws by sharing common board members.

The resignation won’t make that investigation disappear. In a statement Monday afternoon, Richard Feinstein, director of the F.T.C.’s Bureau of Competition, commended the companies for acknowledging “that sharing directors raises competitive issues.” But he said the agency would continue to investigate the remaining overlap between the companies’ boards.

Google and Apple still share one board member, Arthur Levinson, the chairman of Genentech.

Mr. Schmidt’s resignation from Apple’s board constitutes a stark admission  Apple and Google had previously played down the issue  that the companies are now directly competing in the crucial race to develop the next generation of software for mobile phones and personal computers.