Flapping flight is more maneuverable than steady flight. It is debated whether this advantage is necessarily accompanied by a trade-off in the flight efficiency. Here we ask if any flapping motion exists that is aerodynamically more efficient than the optimal steady motion. We solve the Navier-Stokes equation governing the fluid dynamics around a 2D flapping wing, and determine the minimal aerodynamic power needed to support a specified weight. While most flapping wing motions are more costly than the optimal steady wing motion, we find that optimized flapping wing motions can save up to 27% of the aerodynamic power required by the optimal steady flight. We explain the cause of this energetic advantage. © 2009 The American Physical Society.