  Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the
nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a
quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$
the smooth contragredient of $\pi$, and by $\pi^{\sigma}$ the representation
$\pi\circ \sigma$, we show that the representation of $GL(2n, K)$ obtained by
normalized parabolic induction of the representation $\pi^\vee \otimes
\pi^\sigma$ is distinguished with respect to $GL(2n,F)$. This is a step towards
the classification of distinguished generic representations of general linear
groups over $p$-adic fields.
