  The construction of nonlocal sets of quantum states has attracted much
attention in recent years. We first introduce two Lemmas related to the
triviality of orthogonality-preserving local measurements. Then we propose a
general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in
$(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states
are also put forward for the multipartite quantum systems with arbitrary
dimensions. Our novel construction gives rise to nonlocal sets of orthogonal
product states with much less members and thus reveals the phenomenon of
nonlocality without entanglement more efficiently.
