Epitaxial orthorhombic HoMnO 3 films were grown on Nb-doped SrTiO 3 (001) single-crystal substrates. X-ray diffractometry showed a uniform crystallographic orientation with the c axis along the substrate normal and an anisotropic compressive stress along the b axis of the Pbnm structure. The magnetization of the films was dominated by the paramagnetism of the Ho 3+ ions; the latter showed a strong anisotropy with respect to the in-plane and perpendicular-to-plane magnetic field direction. The rotational anisotropy of the magnetoelectric effect was measured for magnetic field rotation in the (110) o , (110) o , and (001) o planes. Whereas magnetic field rotation in the (110) o and (110) o planes showed a twofold pattern with the smallest magnetoelectric effect observed in magnetic fields along the c axis, in-plane (001) o magnetic field rotations revealed an intricate rotational symmetry. A magnetic-field-induced crossover was observed from a low-field region with fourfold rotation patterns to a high-field region with rotation patterns up to the 12th order. This complex rotational symmetry arises from spin-orbit coupling of the Ho 3+ moments that induces a modulation of the magnetoconductance as well as a magnetoelectric effect through the Maxwell-Wagner mechanism.