Google (NASDAQ:GOOG) CEO Eric Schmidt has held a seat on Apple's (NASDAQ:AAPL) board of directors since 2006. It's probably high time for him to get out of that boardroom.

Two months ago, the Federal Trade Commission started looking into the high-level Google-to-Apple connection. At the time, the companies competed in several important product categories: iPhone versus Android in cell phone software, Safari and Chrome in Web browsers, and MobileMe against Gmail in email software. Schmidt had to recuse himself from any discussions on iPhone strategy, for example.

And now pretty much all of Apple is facing competition from Google. The just-announced Chrome operating system is up against Mac OS X, with a stated goal to "to power computers ranging from small netbooks to full-size desktop systems."

Of course, there's nothing wrong with cross-pollination within the IT industry, or any other sector, for that matter. For example, Intel (NASDAQ:INTC) CEO Paul Otellini has a board seat with Google, and seems unlikely ever to face direct competition from Big G. Netflix (NASDAQ:NFLX) CEO Reed Hastings holds a seat on Microsoft's (NASDAQ:MSFT) board -- another case of cooperation rather than competition. Likewise, Yahoo! (NASDAQ:YHOO) has sent top executives and board members Jerry Yang and Carol Bartz to lend a hand with Cisco Systems' (NASDAQ:CSCO) strategic direction. There's little overlap between those two businesses today, though that might change.

But you can take it too far, and that's what's happening in Cupertino. Schmidt can advise Apple on iPod strategy now, I guess. Maybe he can talk strictly about the hardware side of the Mac business, too. Pretty much everything else seems to be off limits. It's time to step down and give that tenth board seat to an advisor who can lend expertise to more than just a niche or two of Apple's business.

For much the same reasons, Arthur Levinson might want to leave one of these two boards. The CEO of Genentech before it became a part of Swiss pharma giant Roche Holding is a longtime director of both Apple and Google, and faces many of Schmidt's potential conflicts of interest. Former Vice President Al Gore is another fence-sitter, being an Apple board member and a senior Google advisor.

If Eric wants to hobnob with his peers at Apple, he can invite them to an informal chat at the excellent Google cafeterias -- the two headquarters are only fifteen minutes apart. But that formal board seat is looking mighty wobbly now.

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