The paper describes a method for estimation of the orientation of 3D objects without point correspondence information. It is based on decomposition of the object onto a basis of spherical harmonics. Tensors are obtained, and their normalization provides the orientation of the object. Theoretical and experimental results show that the approach is more accurate than the classical method based on the diagonalisation of the inertia matrix. Fast registration of 3D objects is a problem of practical interest in domains such as robotics and medical imaging, where it helps to compare multimodal data.