An algorithm is raised to deal with waveguide step discontinuity problems by using various new basis functions in the expansion of the fields at the discontinuity to solve the scattering parameters.The electromagnetic field's edge condition in the vicinity of metal wedges is generally taken into account and modified trigonometric functions are constructed as basis functions to expand the electromagnetic fields at the discontinuity.Matching the tangential fields over the common aperture can form a set of linear equations.Very good numerical convergence is observed.Furthermore

some different basis functions are constructed and evaluated

and the excellent convergence property is also obtained.For one discontinuity

the order of the linear equations is the same as the number (a few or only one) of the basis functions.This keeps the equations at the lowest order and the numerical computation efficiency is thus improved drastically.