  This paper concerns a super Poisson-Lie structure on the real Lie supergroup
$SU(m \ve n)$. In fact, it turns out that the realification of the complex Lie
supergroup $SL(m \ve n, \C)$ is a double of $SU(m \ve n)$ i.e. it is endowed
with a structure of super Poisson-Lie which brings down on the supergroup $SU(m
\ve n)$. We show that the dual Poisson-Lie supergroup of $SU(m\ve n)$ is
$s(AN)$. Reciprocaly, $s(AN)$ inherits a super Poisson-Lie structure from the
realification of $SL(m\ve n,\C)$ such that its dual Poisson-Lie supergroup is
$SU(m\ve n)$.
