Let $u$ be an inner function and $K_u^2$ be the corresponding model space. For an inner function $v$, the subspace $v{H}^2$ is an invariant subspace of the unilateral shift operator on $H^2$. In this article, using the structure of a Toeplitz kernel $\ker T_{\overline{u}v}$, we study the intersection $K_u^2\cap v{H}^2$ by properties of inner functions $u$ and $v$$(v...$