The analysis of a step discontinuity of single-mode slab waveguide excited in the dominant mode is presented for both TE- and TM-modes. The problem is formulated by using the mode-matching procedure parallel to that of Marcuse. The solutions for the reflection coefficient, transmitted power and radiated power are then obtained by the application of the residue-calculus technique, which leads to more general expressions than those so far obtained by others who used more complicated methods. Numerical results are given which are in good agreement with previous results for specific cases. For the general case, the results also agree very well with those obtained by the reciprocity theorem.