Radiation is a primary concern in the planning of a manned mission to Mars. Recent studies using NASA Langley Research Center's HZETRN space radiation transport code show that the low energy neutron fluence on the Martian surface is larger than previously expected. The upper atmosphere of Mars is exposed to a background radiation field made up of a large number of protons during a solar particle event and mixture of light and heavy ions caused by galactic cosmic rays at other times. In either case, these charged ions interact with the carbon and oxygen atoms of the Martian atmosphere through ionization and nuclear collisions producing secondary ions and neutrons which then interact with the atmospheric atoms in a similar manner. In the past, only these downward moving particles have been counted in evaluating the neutron energy spectrum on the surface. Recent enhancements in the HZETRN code allow for the additional evaluation of those neutrons created within the Martian regolith through the same types of nuclear reactions, which rise to the surface. New calculations using this improved HZETRN code show that these upward moving neutrons contribute significantly to the overall neutron spectrum for energies less than 10 MeV.