  In a recent article [Phys. Rev. A 54, 1793 (1996)] Krenn and Zeilinger
investigated the conditional two-particle correlations for the subensemble of
data obtained by selecting the results of the spin measurements by two
observers 1 and 2 with respect to the result found in the corresponding
measurement by a third observer. In this paper we write out explicitly the
condition required in order for the selected results of observers 1 and 2 to
violate Bell's inequality for general measurement directions. It is shown that
there are infinitely many sets of directions giving the maximum level of
violation. Further, we extend the analysis by the authors to the class of
triorthogonal states |Psi> = c_1 |z_1>|z_2>|z_3> + c_2 |-z_1>|-z_2>|-z_3>. It
is found that a maximal violation of Bell's inequality occurs provided the
corresponding three-particle state yields a direct ("all or nothing")
nonlocality contradiction.
