  Let $G$ be the group of $F$-points of a split connected reductive $F$-group
over a non-Archimedean local field $F$ of characteristic 0. Let $\pi$ be an
irreducible smooth self-dual representation of $G$. The space $W$ of $\pi$
carries a non-degenerate $G$-invariant bilinear form $(\,,\,)$ which is unique
up to scaling. The form is easily seen to be symmetric or skew-symmetric and we
set $\varepsilon({\pi})=\pm 1$ accordingly. In this article, we show that
$\varepsilon{(\pi)}=1$ when $\pi$ is a generic representation of $G$ with
non-zero vectors fixed under an Iwahori subgroup $I$.
