  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 pairpurification (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.
