  In this note we develop a half-space model for the pseudo-hyperbolic space
$\mathbb{H}^{p,q}$, for any $p,q$ with $p\geq 1$. This half-space model embeds
isometrically onto the complement of a degenerate totally geodesic hyperplane
in $\mathbb{H}^{p,q}$. We describe the geodesics, the totally geodesic
submanifolds, the horospheres, the isometry group in the half-space model, and
we explain how to interpret the boundary at infinity in this setting.
