  We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to multipartite d-dimensional systems. All the Bell
inequalities based on this generalization take the same simple form as the CHSH
inequality. For small systems, numerical results show that the new inequalities
are tight and we believe this is also valid for higher dimensional systems.
Moreover, the new inequalities are relevant to the previous ones and for
bipartite system, our inequality is equivalent to the
Collins-Gisin-Linden-Masser-Popescu (CGLMP) inequality.
