  We prove a half-space theorem for an ideal Scherk graph $\Sigma\subset
M\times\mathbb R$ over a polygonal domain $D\subset M,$ where $M$ is a Hadamard
surface whose curvature is bounded above by a negative constant. More
precisely, we show that a properly immersed minimal surface contained in
$D\times\mathbb R$ and disjoint from $\Sigma$ is a translate of $\Sigma.$
