  In this article, we prove that if $\Pi: X\to \Omega$ is a surjective
holomorphic map, with $\Omega$ a Stein space and $X$ a complex manifold of
dimension $n\geq 3,$ and if, for every $x\in \Omega$ there exists an open
neighborhood $U$ such that $\Pi^{-1}(U)$ is Stein, then $X$ is Stein
