  We study conditions for the deterministic transformation
$\ket{\psi}\longrightarrow\ket{\phi}$ of a bipartite entangled state by a
separable operation. If the separable operation is a local operation with
classical communication (LOCC), Nielsen's majorization theorem provides
necessary and sufficient conditions. For the general case we derive a necessary
condition in terms of products of Schmidt coefficients, which is equivalent to
the Nielsen condition when either of the two factor spaces is of dimension 2,
but is otherwise weaker. One implication is that no separable operation can
reverse a deterministic map produced by another separable operation, if one
excludes the case where the Schmidt coefficients of $\ket{\psi}$ and are the
same as those of $\ket{\phi}$. The question of sufficient conditions in the
general separable case remains open. When the Schmidt coefficients of
$\ket{\psi}$ are the same as those of $\ket{\phi}$, we show that the Kraus
operators of the separable transformation restricted to the supports of
$\ket{\psi}$ on the factor spaces are proportional to unitaries. When that
proportionality holds and the factor spaces have equal dimension, we find
conditions for the deterministic transformation of a collection of several full
Schmidt rank pure states $\ket{\psi_j}$ to pure states $\ket{\phi_j}$.
