On the basis of recent observations that pickup ions are inefficiently scattered through 90¿ pitch angle, a pickup ion transport model has been developed which assumes that pickup ion distributions are uniform in the so-called forward and reverse hemispheres, containing ions with pitch angles less than 90¿ and greater than 90¿, respectively. A simple, fast numerical scheme is then described which solves the transport equations. Several examples are solved and comparisons are performed between the numerical solutions and previously used analytical solutions. Results from the model are then compared to pickup ion spectra obtained with the solar wind ion composition spectrometer on the Ulysses satellite. ¿ 1998 American Geophysical Union