  It is known that the structure of invariant subspaces of the Hardy space
$H^2(\mathbb D^n)$ on the polydisc $\mathbb{D}^n$ is very complicated; hence,
we need good examples help us to understand the structure of invariant
subspaces of $H^2(\mathbb D^n)$. In this paper, we define two types of
invariant subspaces of $H^2(\mathbb D^n)$. Then, we give a characterization of
these types invariant subspaces in view of the Beurling-Lax-Halmos Theorem.
Unitary equivalence is also studied in this paper.
