A time independent semiclassical surface hopping model was previously derived for the numerical evaluation of the transition amplitudes for multisurface problems. This analysis is revisited and a new method incorporating phase information disregarded by the previous model is derived. The coordinate axis is partitioned into a finite number of intervals. The propagation of the wavefront across an interval is again described by a flux conserving transformation. For the one dimensional case transition amplitudes across many intervals can be evaluated via matrix multiplication of the individual interval transforms. Comparison with exact quantum mechanical calculations show that the results generated by this new model are highly accurate. Further this new approach offers a significant increase in computational efficiency. Accurate results can be obtained in calculations employing larger and hence fewer intervals to partition the system where the original model fails. This increase in efficiency has important implications for multidimensional surface hopping problems. (C) 2003 American Institute of Physics.