A novel transfer matrix method is employed for the analysis of polarization rotation in an asymmetrically periodically loaded rib waveguide. The transfer matrix method is based on the hybrid local normal modes. The vector normal modes are approximated by a linear combination of the scalar modes. In comparison with the coupled-mode analysis, this approach takes the radiation loss due to scattering at the junctions of the periodic loading into account. A new simple analytical solution in the power coupling for the periodically loaded rib waveguide is derived. Analytic results are shown for some typical structure and compared with results by more rigorous numerical methods.