A single-domain particle with general quadratic anisotropy energy, of crystalline or magnetostatic origin, is shown to have at most one metastable orientation of its magnetization in the presence of an external magnetic field. A reliable and efficient numerical algorithm is given for the determination of the orientation of the magnetization in the stable and metastable states, and a method of determining whether or not a metastable state exists by monitoring iteration for the metastable state is explained. The proposed algorithm is also efficient in the special case of uniaxial anisotropy. © 1990, IEEE. All rights reserved.