SAN FRANCISCO—In a move that severs another tie between Google and Apple, Arthur D. Levinson, the former chief executive of Genentech, has resigned from Google's board.

In a statement on Monday, Google gave no reason for Levinson's departure, but earlier this year, the Federal Trade Commission began an antitrust investigation into the close ties between the boards of Google and Apple.

At the time, Levinson and Eric E. Schmidt, Google's chief executive, were directors of both Google and Apple. The Clayton Antitrust Act of 1914 prohibits such board overlaps when they reduce competition between two rival companies.

Schmidt resigned from the Apple board in August.

In a statement, Jon Leibowitz, the chairman of the commission, suggested that the commission had been ready to go to court to force the two companies to sever their board ties.

“;Google, Apple and Mr. Levinson should be commended for recognizing that overlapping board members between competing companies raise serious antitrust issues, and for their willingness to resolve our concerns without the need for litigation,”; Leibowitz said. “;Beyond this matter, we will continue to monitor companies that share board members and take enforcement actions where appropriate.”;

Two other Apple directors, former Vice President Al Gore and Bill Campbell, chairman of Intuit, remain advisers to Google. But the commission said it was no longer pursuing its inquiry into the two companies' connections.

When Apple appointed Schmidt to its board in 2006, the move was seen as cementing an alliance between two Silicon Valley giants with a common enemy: Microsoft. But as Google's business continued to expand into new areas, it began bumping up against the interests of Apple with growing frequency, fraying the ties between the two allies.

Apple entered the cell phone business when it introduced the iPhone in January 2007. Google followed suit 10 months later, when it unveiled its Android software for mobile phones.

The growing tension between the two companies came into public view recently when Google accused Apple of rejecting a proposed Google Voice application for the iPhone. Apple has said it is still reviewing the application. The dispute has drawn scrutiny from the Federal Communications Commission.

Google and Apple also compete in other areas, including Web browsers, photo-editing software and the distribution of music and video on Apple's iTunes Store and Google's YouTube. And Google is preparing an operating system for lightweight computers that could compete with the Macintosh operating system.

When Schmidt quit Apple's board, Steve Jobs, that company's chief executive, noted that if Schmidt had stayed, his effectiveness as a director would have been diminished because he would “;have to recuse himself from even larger portions of our meetings due to potential conflicts of interest.”;

Earlier this month, however, Schmidt insisted that Levinson should remain on both boards despite the inquiry, saying that the revenue that Apple and Google received from competing products was below a legal threshold.

Under the Clayton Act, so-called interlocking directorates are not considered a problem if the revenue from products in which the companies compete is less than 2 percent of either company's sales.