  We prove that each nonpositively curved square VH-complex can be turned
functorially into a locally 6-large simplicial complex of the same homotopy
type. It follows that any group acting geometrically on a CAT(0) square
VH-complex is systolic. In particular the product of two finitely generated
free groups is systolic, which answers a question of Daniel Wise. On the other
hand, we exhibit an example of a compact non-VH nonpositively curved square
complex, whose fundamental group is neither systolic, nor even virtually
systolic.
