  We derive a sufficient condition for a set of pure states, each entangled in
two remote $N$-dimensional systems, to be transformable to
$k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local
operations and classical communication. If $k=N$, the condition is also
necessary. This condition reveals the function of the relative marginal density
operators of the entangled states in the entanglement manipulation without
sufficient information of the initial states.
