  We provide a method for checking indistinguishability of a set of
multipartite orthogonal states by local operations and classical communication
(LOCC). It bases on the principle of nonincreasing of entanglement under LOCC.
This method originates from the one introduced by Ghosh \emph{et al.} (Phys.
Rev. Lett. \textbf{87}, 5807 (2001) (quant-ph/0106148)), though we deal with
{\emph pure} states. In the bipartite case, our method is operational, although
we do not know whether it can always detect local indistinguishability. We
apply our method to show that an arbitrary complete multipartite orthogonal
basis is indistinguishable if it contains at least one entangled state. We also
show that probabilistic distinguishing is possible for full basis if and only
if all vectors are product. We employ our method to prove local
indistinguishability in a very interesting example akin to "nonlocality without
entanglement".
