  Let $F$ be a $p$-adic field ($p\neq 2$), let $E$ be a quadratic Galois
extension of $F$, and let $n \geq 2$. We construct representations in the
discrete spectrum of the $p$-adic symmetric space $H \backslash G$, where $G =
\mathbf{GL}_{2n}(E)$ and $H = \mathbf{U}_{E/F}(F)$ is a quasi-split unitary
group over $F$.
