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New boundary integral equation method which was previously proposed have been examined in detail and extended to the computer-aided design (CAD) of asymmetrical dielectric slab waveguide bends. Many numerical results of symmetric waveguide discontinuities and asymmetric waveguide bends confirm the validity of the new method. They show that all numerical results satisfy the energy conservation law within an accuracy of 1% and indicate that the new integral equation method is very suitable for the basic theory or a solver of CAD software for various open dielectric waveguide circuits.