Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equation
f(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G;
when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact. Some solutions are given by the same formulas as in the known abelian case. The new ones are expressed in terms of matrix-coeffcients of irreducible, 2-dimensional representations of G and of solutions of Wilson's functional equation phi(xy) +phi(xy(-1)) = 2 phi(x)gamma(y).
