  The lattice of (001)-oriented BiFeO$_3$ epitaxial thin film has been
identified by synchrotron x-ray diffraction. By choosing proper scattering
zones containing the fixed (001) reflection, we have shown that low-symmetry
phases similar to a $M_A$ phase exist in the thin film at room temperature.
These results demonstrate a change in phase stability from rhombohedral in bulk
single crystals, to a modified monoclinic structure in epitaxial thin films.
