  In this paper we study the nonlocal properties of two-qubit Werner states
parameterized by the visibility parameter 0<p<1. New family of Bell
inequalities are constructed which prove the two-qubit Werner states to be
nonlocal for the parameter range 0.7056<p<1. This is slightly wider than the
range 0.7071<p<1, corresponding to the violation of the
Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by
Gisin in the positive, i.e., there exist Bell inequalities which are more
efficient than the CHSH inequality in the sense that they are violated by a
wider range of two-qubit Werner states.
