  Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over
a non-archimedean local field of characteristic zero. Let $\pi$ be an
irreducible admissible smooth representation of $G$. It is well known that the
contragredient of $\pi$ is isomorphic to a twist of $\pi$ by an automorphism of
$G$. We prove a similar result for double covers of $G$ which occur in the
study of local theta correspondences.
