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Burkhead ran for 344 yards and two touchdowns while cathicng 17 passes for 145 yards last season, when his playing time increased following the knee injury of Giovani Bernard.
His departure leaves the team with the rehabbing Bernard, fourth-year veteran Jeremy Hill and second-year man Tra Carson as running backs on the roster.
Bernard is not expected to be ready when the season begins.
Cedric Peerman, also a special teams standout, is a free agent.
The Bengals previously lost tackle Andrew Whitworth (Los Angeles Rams), guard Kevin Zeitler (Cleveland Browns), defensive end Margus Hunt (Indianapolis Colts) and defensive tackle Domata Peko (Denver Broncos) as free agents this month.
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