LONDON -- Barclays (LSE: BARC.L) fell 2% to 155 pence this morning after Sir Michael Rake confirmed he did not wish to be considered for the role of chairman at the bank.

Sir Michael, a nonexecutive at Barclays since 2008, had been seen as a frontrunner to replace Marcus Agius, who tendered his resignation in the wake of the LIBOR scandal earlier this month. Agius is currently the bank's interim executive chairman following the departure of chief executive Bob Diamond. Sir Michael's confirmation was issued by easyJet (LSE: EZJ.L), the low-cost airline that Sir Michael has chaired since 2010.

Weekend press reports suggested that major Barclays shareholders have demanded an external candidate be appointed for the 750,000 pound-a-year position.

On Friday, Sir Stelios Haji-Ioannou, 37% owner of easyJet, published a letter urging fellow shareholders to oust Sir Michael from the airline's board. Sir Stelios reckoned Sir Michael had "too many jobs ... requiring extensive oversight" and could not devote enough time to easyJet.

Sir Stelios claimed Sir Michael collected a 300,000 pound annual fee for working at the airline for just one day a week. Sir Michael's other jobs include the chairmanship of BT, a position he has held since 2007 and which pays 650,000 pounds a year.

While easyJet said today that it repeated its support for Sir Michael, any business that has a suspected "fat cat" at its helm might not be the most dependable investment this choppy market has to offer right now.

Indeed, if you are seeking management that provides somewhat better value, The Motley Fool has produced a special free report that could assist your investment decisions. "The One UK Share Warren Buffett Loves" reveals the favorite FTSE 100 name held by Warren Buffett -- the billionaire U.S. investor who has thrashed the markets during the last five decades or so. As you may already know, Mr. Buffett has always demanded high-quality boardrooms at his chosen investments. The Fool's exclusive Warren Buffett report can be downloaded immediately, but hurry -- the report is free for a limited time only.      

Barclays issues its half-year results on Friday.

Investing is by no means easy in today's uncertain economy. That's why we've published "Top Sectors for 2012" -- our guide to three favorable industries. This free report will be dispatched immediately to your inbox.

Further Motley Fool investment opportunities: