  In this paper, we mainly study the local indistinguishability of multipartite
product states. Firstly, we follow the method of Z.-C. Zhang \emph{et al}[Phys.
Rev. A 93, 012314(2016)] to give another more concise set of $2n-1$ orthogonal
product states in $\mathbb{C}^m\otimes\mathbb{C}^n(4\leq m\leq n)$ which can
not be distinguished by local operations and classical communication(LOCC).
Then we use the 3 dimension cubes to present some product states which give us
an intuitive view how to construct locally indistinguishable product states in
tripartite quantum system. At last, we give an explicit construction of locally
indistinguishable orthogonal product states for general multipartite system.
