  We argue that the centrosymmetric $C2/c$ symmetry in BiMnO$_3$ is
spontaneously broken by antiferromagnetic (AFM) interactions existing in the
system. The true symmetry is expected to be $Cc$, which is compatible with the
noncollinear magnetic ground state, where the ferromagnetic order along one
crystallographic axis coexists with the the hidden AFM order and related to it
ferroelectric polarization along two other axes. The $C2/c$ symmetry can be
restored by the magnetic field $B \sim 35$ Tesla, which switches off the
ferroelectric polarization. Our analysis is based on the solution of the
low-energy model constructed for the 3d-bands of BiMnO$_3$, where all the
parameters have been derived from the first-principles calculations. Test
calculations for isostructural BiCrO$_3$ reveal an excellent agreement with
experimental data.
