  We derive a multipartite generalized Bell inequality which involves the
entire range of settings for each of the local observers. Especially, it is
applied to show non-local behavior of a six-qubit mixture of
Greenberger-Horne-Zeilinger correlations stronger than previous Bell
inequalities. For certain noise admixture to the correlations an explicit local
realistic model exists in the case of a standard Bell experiment. Bell
experiments with many local settings reveal the non-locality of the state. It
turns out that the new inequality is more stringent than many other Bell
inequalities in the specific quantum state.
