  Suppose that we have two entangled states $\ket {\phi_1}$, $\ket{\psi_1}$
that cannot be converted to any of other two states $\ket{\phi_2}$,
$\ket{\psi_2}$ by local operations and classical communication. We analyze the
possibility of locally transforming a superposition of $\ket{\phi_1}$ and
$\ket{\psi_1}$ into a superposition of $\ket{\phi_2}$ and $\ket{\psi_2}$. By
using the Nielsen's theorem we find the necessary and sufficient conditions for
this conversion to be performed.
