The theory of H^2(D^2) plays a crucial role in both analytic function space theory and multivariable operator theory. It focuses primarily on the structure of submodules and quotient modules,  and two pairs of commuting operators that are naturally associated with submodules and quotient modules. This talk aims to give an interesting construction for the submodule in the Hardy space over the bidisc. For any submodule M in H^2(D^2), we can construct a submodule M_1 in M (maybe be zero subspace) by the self-commutators for the pair (R_z, R_w), and it can be proved that M_1 is either a Beurling-type submodule or 0. So we naturally want to find sufficient conditions such that M_1 is nontrivial. We will highlight the interesting construction and some recent results, as well as unsolved problems. This is based on the joint work with Yufeng Lu and Rongwei Yang.