Let $M$ be a pseudo-convex hypersurface of finite type in $\mathbb {C}^n$, $n \geq 3$, and $\omega $ be an open subset in $M$ such that the boundary of $\omega $ is the transversal intersection of $M$ with a Levi-flat hypersurface $M_0$. We proved the semi-global existence theorems of the tangential Cauchy-Riemann equations $\overline {\partial }_b$ on $\omega $ for $\overline {\partial }_b$-closed $(O, n-2)$ forms satisfying an additional compatibility condition.