  We prove a boundary version of the open mapping theorem for holomorphic maps
between strongly pseudoconvex domains. That is, we prove that the local image
of a holomorphic map $f:D\to D'$ close to a boundary regular contact point
$p\in \de D$ where the Jacobian is bounded from zero along normal
non-tangential directions has to eventually contain every cone (and more
generally every admissible region) with vertex at $f(p)$.
