  This is a second part of alg-geom/9611015. We construct a natural
hyperkaehler desingularization for all singular hyperkaehler varieties. The
desingularization theorem was proven in alg-geom/9611015 under additional
assumption of local homogeneity. Here we show that local homogeneity is
redundant: every singular hyperkaehler variety has locally homogeneous
singularities.
