In this paper, we show that for a connected compact Lie group to be acceptable, it is necessary and sufficient its derived subgroup isomorphic direct product of the groups $${\text {SU}}(n)$$ , {Sp}}(n)$$ {SO}}(2n+1)$$ {G}}_2$$ {SO}}(4)$$ . We there are invariant functions on {SO}}_{4}({\mathbb {C}})^{2}$$ which not generated by 1-argument invariants, though {C}})$$ acceptable.