  Let $H^n$ be the hyperbolic n-space with $n\geq 2$. Suppose that $\Gamma<Isom
H^n$ is a discrete, torsion free subgroup and $a$ is a point in the domain of
discontinuity $\Omega(\Gamma)$. Let $p$ be the projection map from $H^n$ to the
quotient manifold $M=H^n/\Gamma$. In this paper we prove that there exists an
open neighborhood $U$ of $a$ in $H^n\cup\Omega(\Gamma)$ such that $p$ is an
isometry on $U\cap H^n$.
