The Wess-Zumino term H is studied on the sigma model manifold M with a group action fg, g is an element of the group G. fg is a symmetry of the Wess-Zumino term provided that f*gH=H and C(g, ( phi ))=1. C(g, ( phi )) is a group homomorphism from G to U(1) and ( phi ) is the homotopy class of the sigma model map phi . If phi is contractible to a constant map, it is shown that C(g, ( phi ))=1.