  We classify the compact quantum groups $A_u(Q)$ (resp. $B_u(Q)$) up to
isomorphism when $Q>0$ (resp. when $Q \bar{Q} \in {\mathbb R} I_n$). We show
that the general $A_u(Q)$'s and $B_u(Q)$'s for arbitrary $Q$ have explicit
decompositions into free products of these special $A_u(Q)$'s and $B_u(Q)$'s.
