A new scheme is proposed for realizing entanglement swapping in cavity QED. The scheme is based on the resonant interaction of two-mode cavity with Λ-type three-level atom, and it involves only a single measurement. In the scheme, the output state after swapping is exactly the maximally entangled state in principle, thus it is prior to the previous one, in which the output state is just approximate. Calculations indicate that our scheme is less influenced by an error.