  In this paper, we investigate space-like graphs defined over a domain
$\Omega\subset M^{n}$ in the Lorentz manifold $M^{n}\times\mathbb{R}$ with the
metric $-ds^{2}+\sigma$, where $M^{n}$ is a complete Riemannian $n$-manifold
with the metric $\sigma$, $\Omega$ has piecewise smooth boundary, and
$\mathbb{R}$ denotes the Euclidean $1$-space. We can prove an interesting
stability result for translating space-like graphs in $M^{n}\times\mathbb{R}$
under a conformal transformation.
