Measurements of the dependence of the 235U fission cross section on neutron energy were carried out in the energy range from 35 keV to 3.5 MeV. Three different techniques were applied to monitor the neutron flux. The 6Li(n,α)T cross section was utilized in the lower energy range (<110 keV). The grey neutron detector was employed in the entire energy range, and the black neutron detector was used above 400 keV. The shapes were normalized with the results obtained from three different sets of absolute cross-section measurements. The associated activity technique was applied in the 450- to 650-keV range, the black neutron detector was used for absolute flux measurements at 800 keV and 3.5 MeV, and a calibrated vanadium bath was used at 500 keV. The results from the present measurements agree well with more recent data obtained by other experimenters but differ up to a factor of 2 from older values.