  Resonant x-ray scattering is performed near the Mn K-absorption edge for an
epitaxial thin film of BiMnO3. The azimuthal angle dependence of the resonant
(003) peak (in monoclinic indices) is measured with different photon
polarizations; for the $\sigma\to\pi'$ channel a 3-fold symmetric oscillation
is observed in the intensity variation, while the $\sigma\to\sigma'$ scattering
intensity remains constant. These features are accounted for in terms of the
peculiar ordering of the manganese 3d orbitals in BiMnO3. It is demonstrated
that the resonant peak persists up to 770 K with an anomaly around 440 K; these
high and low temperatures coincide with the structural transition temperatures,
seen in bulk, with and without a symmetry change, respectively. A possible
relationship of the orbital order with the ferroelectricity of the system is
discussed.
