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An eigenmode of a magnetooptical planar waveguide is studied for the case of the magnetization direction perpendicular to the waveguide axis. The planar waveguide can be composed of an arbitrary number of isotropic, anisotropic or magnetooptical layers, provided that the local optical axes are parallel to the laboratory coordinate frame de ned by the waveguide axis and the normal to the waveguide plane. For this kind of device structure, Maxwell's equations can be solved for one component of the electric eld and one component of the magnetic eld. The resulting coupled set of equations is linear in the propagation constant, and the eigenmode can be easily obtained using canned numerical routines.