The 233U fission cross section was measured at a well-collimated short flight path of the CBNM Linac from 50 eV to below thermal energy for a direct normalization to the 2200 m/sec reference cross section. The fission reaction rate and the neutron spectrum were determined simultaneously with solid state detectors placed on each side of a back-to-back 233U-10B layer. From the counting-rate ratios σƒ curves were calculated assuming a 1/ behavior of the 10B(n,α)7 Li cross section. Several fission and resonance integrals were calculated from the normalized σƒ curve and compared with other published results. Moreover, the Westcott gƒ factor was calculated from our data in order to check the shape of the fission cross section below 1 eV. Furthermore, we propose a common normalization procedure based on the fission integral obtained from our measurements.