The cross sections for neutron-induced fission of 235U, 238U, 209Bi, and natPb in the intermediate-energy region were measured using parallel plate fission ionization chambers. The experiments were carried out relative to the differential n-p scattering cross section using quasi-monoenergetic neutron beams with peak energies ranging from 33 to 200 MeV. The experimental cross sections were compared to International Nuclear Data Committee reference fission cross sections, to results of nuclear model calculations, and to cross sections calculated with the nuclear models implemented in the radiation transport code MCNPX. The experimental results for 235U and 209Bi are consistent with the available reference cross sections and theoretical data while the 238U(n,f) cross section exceeds the reference cross section systematically by ~7% between 30 and 60 MeV. The experimental results for natPb agree with a parameterization of other experimental data for natPb(n,f).