  Let $G$ be a compact Lie group with a maximal torus $T$. Based on a
presentation of the integral cohomology ring $H^{\ast}(G/T)$ of the flag
manifold $G/T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit and
unified construction of the integral cohomology rings $H^{\ast}(G)$ for the
$1$--connected Lie groups $G$. In this paper we extend this construction to all
compact Lie groups.
