For planar dielectric waveguides, it has been previously demonstrated that radiation modes with the same propagation constant constitute a two-dimensional vectorial space. Presented is an exact simplified technique for the orthogonalization of radiation modes. This method is based on the representation of such modes in terms of plane waves. It is shown that the infinite portion of the normalization integral is sufficient for determining the coefficients of a radiation mode that is orthogonal to an arbitrary initial radiation mode.