  It is well known that any entangled mixed state in $2\otimes 2$ systems can
be purified via infinite copies of the mixed state. But can one distill a pure
maximally entangled state from finite copies of a mixed state in any bipartite
system by local operation and classical communication? This is more meaningful
in practical application. We give a necessary and sufficient condition of this
distillability. This condition can be expressed as: there exists
distillable-subspaces. According to this condition, one can judge whether a
mixed state is distillable or not easily. We also analyze some properties of
distillable-subspaces, and discuss the most efficient purification protocols.
Finally, we discuss the distillable enanglement of two-quibt system for the
case of finite copies.
