  Any pure entangled state of two particles violates a Bell inequality for
two-particle correlation functions (Gisin's theorem). We show that there exist
pure entangled N>2 qubit states that do not violate any Bell inequality for N
particle correlation functions for experiments involving two dichotomic
observables per local measuring station. We also find that
Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for
refutation of local realistic description.
