  In this paper, we mainly characterize the structure of product bases of the
complex vector space
  $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$. It gives an answer to the
conjecture in case of $d=2n$ proposed by McNulty et al in 2016. As the
application of the result, we obtain all the product bases of a bipartite
system $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$. It is helpful to review the
structure of all the product bases of $\mathbb{C}^{2}\bigotimes\mathbb{C}^{2}$
and $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$, which given by McNulty et al.
