  We propose an alternative formulation of the $Z_2$ topological index for
quantum spin Hall systems and band insulators when time reversal invariance is
not broken. The index is expressed in terms of the Chern numbers of the bands
of the model, and a connection with the number of pairs of robust edge states
is thus established. The alternative index is easy to compute in most cases of
interest. We also discuss connections with the recently proposed spin Chern
number for quantum spin Hall models.
