A novel Fourier split-step algorithm for the solution of the parabolic wave equation is proposed. The derivations are based on a two-dimensional linearly bridged knife-edge terrain model that considers ideally conducting as well as dielectric lossy ground together with a dielectric lossy layer as macroscopic representation of vegetation and buildings. The boundary condition at the terrain interface is formulated in the spectral domain, and it is shown that waves with a very wide angular spectrum with respect to the horizontal can accurately be modeled as long as the dominant portion of energy propagates above the terrain. Validation results are given for an ideally conducting as well as lossy dielectric wedge and an ideally conducting rounded obstacle. Also, real-world propagation curves show good agreement with measured data.