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A staggered board is a governance practice in which only a fraction (typically a third) of the members of the board of directors is elected each year, rather than all at once.
Practically, staggered boards have the effect of making hostile takeovers more difficult and are hence considered an anti-takeover practice, similar to a poison pill. In the presence of a staggered board, a hostile bidder must wait several years to entirely replace the board with one of its own choosing, particularly because it must win proxy fights at successive shareholder meetings. 
McDonalds is an example of a company with a staggered board.