  We present the modified relative entropy of entanglement (MRE) in order to
both improve the computability for the relative entropy of entanglement and
avoid the problem that the entanglement of formation seems to be greater than
entanglement of distillation. For two qubit system we derive out an explicit
and "weak" closed expression of MRE that depends on the pure state
decompositions in the case of mixed states. For more qubit system, we obtain an
algorithm to calculate MRE in principle. MRE significantly improves the
computability of relative entropy of entanglement and decreases the dependence
and sensitivity on the pure state decompositions. Moreover it is able to
inherit most of the important physical features of the relative entropy of
entanglement. In addition, a kind of states, as an extension of Werner's
states, is discussed constructively.
