The relative energy dependence of the235U fission cross section has been measured with respect to the (n, p) scattering reaction for neutron energies from 0.8 to 4 MeV. The Lawrence Livermore Laboratory Linac provided a pulsed source of neutrons, and energies were measured by neutron time of flight. The flux monitor consisted of a thin annular polyethylene proton radiator with a shielded recoil detector. The total error in the relative235U (n, f) cross section is<1.5% from 0.8 to 4 MeV.