  The $2$-closure $\overline{G}$ of a permutation group $G$ on $\Omega$ is
defined to be the largest permutation group on $\Omega$, having the same orbits
on $\Omega\times\Omega$ as $G$. It is proved that if $G$ is supersolvable, then
$\overline{G}$ can be found in polynomial time in $|\Omega|$. As a byproduct of
our technique, it is shown that the composition factors of $\overline{G}$ are
cyclic or alternating of prime degree.
