  We study the strong coupling limit of a two-band Hubbard Hamiltonian that
also includes an inter-orbital on-site repulsive interaction $U_{ab}$. When the
two bands have opposite parity and are quarter filled, we prove that the ground
state is simultaneously ferromagnetic and ferroelectric for infinite
intra-orbital Coulomb interactions $U_{aa}$ and $U_{bb}$. We also show that
this coexistence leads to a singular magnetoelectric effect.
