  We present an revised geometric measure of entanglement (RGME). The revised
version is an entanglement monotone. Some useful inequalities about RGME are
deduced. For exemplification, we give the formulas of RGME for the
two-parameter class of states in $2 \otimes n$ quantum system, the two
particles high dimensional maximally entangled mixed state, the isotropic state
including $n$-particle $d$-level case and two multipartite bound entangled
states. The result shows there is a relation $\widetilde{E}_{\sin^2} \leq
E_{re}$, which indicates that the RGME is an appropriate measure of
entanglement.
