  In this work, we study the local distinguishability of maximally entangled
states (MESs). In particular, we are concerned with whether any fixed number of
MESs can be locally distinguishable for sufficiently large dimensions. Fan and
Tian \emph{et al.} have already obtained two satisfactory results for the
generalized Bell states (GBSs) and the qudit lattice states when applied to
prime or prime power dimensions. We construct a general twist-teleportation
scheme for any orthonormal basis with MESs that is inspired by the method used
in [Phys. Rev. A \textbf{70}, 022304 (2004)]. Using this teleportation scheme,
we obtain a sufficient and necessary condition for one-way distinguishable sets
of MESs, which include the GBSs and the qudit lattice states as special cases.
Moreover, we present a generalized version of the results in [Phys. Rev. A
\textbf{92}, 042320 (2015)] for the arbitrary dimensional case.
