Optimal entanglement purifying via entanglement swapping

It is known that entanglement swapping can be used to realize entanglement purifying. By this way, two particles belong to different non-maximally entangled pairs can be projected probabilisticly to a maximally entangled state or to a less entangled state. In this report, we show, when the less entangled state is obtained, if a unitary transformation is introduced locally, then a maximally entangled state can be obtained probabilisticly from this less entangled state. The total successful probability of our scheme is equal to the entanglement of a single pair purification (if two original pairs are in the same non-maximally entangled states) or to the smaller entanglement of a single pair purification of these two pairs ( if two original pairs are not in the same non-maximally entangled states). The advantage of our scheme is no continuous indefinite iterative procedure is needed to achieve optimal purifying. 03.67.-a