A rigorous, versatile and general formulation for the analysis of propagation characteristics of rectangular biaxial anisotropic dielectric waveguide structures with arbitrarily varying indices of refraction profiles is presented. In this formulation the finite-difference method is used for the numerical solution of the wave equation, written in terms of the transverse components of the magnetic field. As a result, a conventional eigenvalue problem is obtained without the presence of the spurious modes (observed in previous formulations), due to the implicit inclusion of the divergence of the magnetic field equal to zero. The theoretical development was used to solve particular problems and the results have shown agreement with those available using other methods.