  Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum
protocols owing to their good property. Thus a lot of attention are paid to how
to construct a nonlocal set of orthogonal product states though it is a
difficult problem. In this paper, we propose a novel general method to
construct a nonlocal set of orthogonal product states in $\mathbb{C}^{d}
\otimes \mathbb{C}^{d}$ for $d\geq3$. We give an ingenious proof for the local
indistinguishability of those product states. The set of product states, which
are constructed by our method, has a very good structure. Subsequently, we give
a construction of nonlocal set of OPSs with smaller members in $\mathbb{C}^{d}
\otimes \mathbb{C}^{d}$ for $d\geq3$. On the other hand, we present two
construction methods of nonlocal sets of OPSs in $\mathbb{C}^{m} \otimes
\mathbb{C}^{n}$, where $m\geq3$ and $n\geq3.$ Furthermore, we propose the
concept of isomorphism for two nonlocal sets of OPSs. Our work is of great help
to understand the structure and classification of locally indistinguishable
OPSs.
