In a general setting, we introduce a new bipartite state property sufficient
for the validity of the perfect correlation form of the original Bell
inequality for any three bounded quantum observables. A bipartite quantum state
with this property does not necessarily exhibit perfect correlations. The class
of bipartite states specified by this property includes both separable and
nonseparable states. We prove analytically that, for any dimension d>2, every
Werner state, separable or nonseparable, belongs to this class.