  We analyze how entanglement between two components of a bipartite system
behaves under the action of local channels of the form $\cE\otimes\cI$. We show
that a set of maximally entangled states is by the action of $\cE\otimes\cI$
transformed into the set of states that exhibit the same degree of
entanglement. Moreover, this degree represents an upper bound on entanglement
that is available at the output of the channel irrespective what is the input
state of the composite system. We show that within this bound the the
entanglement-induced state ordering is ``relative'' and can be changed by the
action of local channels. That is, two states $\varrho_1^{(in)}$ and
$\varrho_2^{(in)}$ such that the entanglement $E[\varrho_1^{(in)}]$ of the
first state is larger than the entanglement $E[\varrho_2^{(in)}]$ of the second
state are transformed into states $\varrho_1^{(out)}$ and $\varrho_2^{(out)}$
such that $E[\varrho_2^{(out)}] > E[\varrho_1^{(out)}]$.
