  We study the closest disentangled state to a given entangled state in any
system (multi-party with any dimension). We obtain the set of equations the
closest disentangled state must satisfy, and show that its reduction is
strongly related to the extremal condition of the local filtering on each
party. Although the equations we obtain are not still tractable, we find some
sufficient conditions for which the closest disentangled state has the same
reduction as the given entangled state. Further, we suggest a prescription to
obtain a tight upper bound of the relative entropy of entanglement in two-qubit
systems.
