  In this paper we show that for a connected compact Lie group to be acceptable
it is necessary and sufficient that its derived subgroup is isomorphic to a
direct product of the groups $\SU(n)$, $\Sp(n)$, $\SO(2n+1)$, $\G_2$, $\SO(4)$.
We show that there are invariant functions on $\SO_{4}(\mathbb{C})^{2}$ which
are not generated by 1-argument invariants, though the group
$\SO_{4}(\mathbb{C})$ is acceptable.
