  Very thick films of BiCrO$_3$ have been grown on a SrTiO$_3$ substrate,
maintaining a tetragonal lattice up to thicknesses of 14,000\AA. Assuming we
can treat films of this thickness as bulk crystals, we first calculated the
experimentally undetermined atomic positions within the unit cell with the
measured lattice constant of the film, then relaxed the lattice constants along
with the atomic positions. All the calculations result in an antiferroelectric
crystal with the {\it Pnma} space group with noncollinear Bi displacements. We
find G-type antiferromagnetism with a spin-orbit induced weak ferromagnetic
component, however, the weak ferromagnetic component can cancel if the
antiferromagnetic spins are oriented along a particular one of the three 2-fold
rotation axes.
