The parabolic equation (PE) model is very useful for many range-dependent acoustic calculations. However, the PE solution breaks down for propagation at large angles, out to long ranges, and in domains in which sound-speed variations are relatively large. This problem was reduced with the introduction of the wide-angle PE of Claerbout, which is based on a rational linear Padé approximation. Generalizing this approach to a sum of rational linear terms [Bamberger et al., SIAM J. Appl. Math. 48, 129–154 (1988)] leads to a higher-order PE that is easy to solve numerically. Calculations will be presented to demonstrate that this higher-order PE accurately handles problems involving very wide angles of propagation and large differences in sound speed including elastic wave propagation involving a superposition of both shear and compresisonal waves.