  From first-principles calculations, we investigate the structural
instabilities of CaMnO$_3$. We point out that, on top of a strong
antiferrodistortive instability responsible for its orthorhombic ground-state,
the cubic perovskite structure of CaMnO$_3$ also exhibit a weak ferroelectric
instability. Although ferroelectricity is suppressed by antiferrodistortive
oxygen motions, we show that it can be favored using strain or chemical
engineering in order to make CaMnO$_3$ multiferroic. We finally highlight that
the FE instability of CaMnO$_3$ is Mn-dominated. This illustrates that,
contrary to the common believe, ferroelectricity and magnetism are not
necessarily exclusive but can be driven by the same cation.
