Google's announcement that it plans to release a new operating system dubbed Chrome has some wondering whether or not Eric Schmidt, the company's CEO, should give up his position on Apple's board of directors. Mr. Schmidt, however, doesn't see any conflict of interest even though his company is working on an operating system that could potentially compete with Mac OS X.

According to the Associated Press, Mr. Schmidt doesn't have any plans to step down from Apple's board, or to excuse himself from meetings that involve discussions about the company's operating system for the Mac.

This isn't the first time Google's CEO has found himself in a potential conflict of interest on Apple's board. Google's Android operating system for smartphones is seen as a competitor to Apple's iPhone, and Mr. Schmidt does stay out of board discussions that involve the combination iPod and smartphone.

The Federal Trade Commission, however, is looking into whether or not Mr. Schmidt's and Arthur Levison's -- an Apple and Google board member -- positions on Apple's board of directors could have a negative impact on competition. If the FTC does see a problem, the men may have to excuse themselves from even more Apple meetings, or potentially step down.

Mr. Schmidt plans to continue with business as usual during the FTC's investigation, and presumably afterwards -- unless the agency tells him otherwise.