  Multipartite entanglement purification is revisited by using the Local
operations and classical communications(LOCCs). We demonstrate our idea by
considering the tripartite case, i.e. the purification of tripartite
entanglement. We express the general tripartite entangled states in a special
representation of total spin operators $J_{123}^{2}$ and $% J_{12}^{2}$ of
tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a
\textit{genuine basis} because it consists of of all the genuine entangled
states of tripartite system. Our protocol is a recurrence one, and only two
copies of the initial mixed tripartite entangled states are needed in each
round. It is shown that if the initial fidelity is larger than a threshold 0.4,
the purification process will succeed.The yield of the current protocol is
higher than the previous multipartite entanglement purification protocols. As a
by-product, we can get a bipartite pure Bell state when the purification
protocol fails for W state. Our protocol also shows that there may be some
special kind of tripartite entanglement which belongs to neither W-type
entanglement nor GHZ-type entanglement.
