We suggest a novel method to determine the sign of cos2 beta in the decays
B --> psiK, by creating interference between K-L and K-S final states via "
regeneration," that is propagation through a matter target region to conver
t some K-L to K-S. The determination of this quantity resolves an ambiguity
between beta and 90 degrees - beta that remains after the standard measure
ments of sin2 beta and may turn out to be important in resolving whether th
e result is in agreement with standard model predictions or indicates the p
resence of new physics. We fmd the measurement is feasible at a B factory,
but requires several years of high-luminosity running with a regeneration t
arget affecting a significant fraction of the detector.