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To the best of the knowledge of the authors, the formulation is carried out for the first time on the finiteelement beam-propagation method for the analysis of the magnetooptic waveguide in which the structure varies dong the propagation direction. The present method is applicable not only to the case in which refractive index difference is small but also to the case for the TE mode and the TM mode propagating in a waveguide with a large refractive index difference. To suppress the spurious reflection from the computational window edges, the transparent boundary condition is applied.