  The structural properties of BiMn$O_3$ were determined from neutron powder
diffraction data as a function of temperature and magnetic field. The structure
at all temperatures was found to be centrosymmetric with space group $C2/c$,
which is incompatible with ferroelectricity. At T$_C\simeq 100 K$, we observed
the onset of a large magnetoelastic strain, proportional to the square of the
magnetization. We interpret this structural rearrangement, together with the
previously observed magnetodielectric anomalies, as due to the need to optimize
the partially frustrated magnetic interactions.
