  Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic
spaces of dimensional $m$ and $n$ corresponding, and given a Holder function
$f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries
of $H^m$ and $H^n$. Then for each $\epsilon >0$ there exists a harmonic map
$u:H^m\to H^n$ which is continuous up to the boundary (in the sense of
Euclidean) and $u|_{\partial H^m}=(f^1,...,f^{n-1},\epsilon)$.
