  In the present paper the cross norm criterion for separability of density
matrices is studied. In the first part of the paper we determine the value of
the greatest cross norm for Werner states, for isotropic states and for Bell
diagonal states. In the second part we show that the greatest cross norm
criterion induces a novel computable separability criterion for bipartite
systems. This new criterion is a necessary but in general not a sufficient
criterion for separability. It is shown, however, that for all pure states, for
Bell diagonal states, for Werner states in dimension d=2 and for isotropic
states in arbitrary dimensions the new criterion is necessary and sufficient.
Moreover, it is shown that for Werner states in higher dimensions (d greater
than 2), the new criterion is only necessary.
