Let $G_n$ be the split classical groups $\Sp(2n)$, $\SO(2n+1)$ and
$\SO(2n)$ defined over a $p$-adic field F or the quasi-split
classical groups $U(n,n)$ and $U(n+1,n)$ with respect to a
quadratic extension $E/F$. We prove the self-duality of unitary
supercuspidal data of standard Levi subgroups of $G_n(F)$ which
give discrete series representations of $G_n(F)$.