We study a special case of the Corona Problem ; let $\Omega $ a bounded domain in $\mathbb {C}^n$ and $f_1, f_2$ two holomorphic functions in $\Omega $ such that $f_1$ is continous in $\overline {\Omega }$, $f_2$ is bounded in $\Omega $ and $|f_1| + |f_2| \geq \delta > 0$. Then we prove that there are $g_1, g_2$ holomorphic and bounded in $\Omega $ so that $f_1g_1 + f_2g_2 = 1$ for some domains including the strictly pseudo-convex ones, the polydisc, the domains of finite type in $\mathbb {C}^2$. We study also the case of stronger regularity assumptions as $\mathcal {C}^k$ and we obtain similar results.