  We consider a special class of two-dimensional discrete equations defined by
relations on elementary NxN squares, N>2, of the square lattice Z^2, and
propose a new type of consistency conditions on cubic lattices for such
discrete equations that is connected to bending elementary NxN squares, N>2, in
the cubic lattice Z^3. For an arbitrary N we prove such consistency on cubic
lattices for two-dimensional discrete equations defined by the condition that
the determinants of values of the field at the points of the square lattice Z^2
that are contained in elementary NxN squares vanish.
