  A set of all states of a bi-partite quantum system can be divided into
subsets each of which contains states with the same degree of entanglement. In
this paper we address a question whether local operations (without classical
communication) affect the entanglement-induced state ordering. We show that
arbitrary unilocal channel (i.e., a channel that acts on one sub-system of a
bi-partite system only) might change the ordering for an arbitrary nontrivial
measure of entanglement. A slightly weaker result holds for the maximally
entangled states. In particular, the maximally entangled states might not
remain the most entangled ones at the output of a unilocal noise channel.
