We measured the fission cross-section ratio of 241Pu relative to 235U over the neutron energy range from 1 keV to 30 MeV at the Lawrence Livermore Laboratory 100-MeV Linac. We used ionization fission chambers and the time-of-flight technique to take data simultaneously over the entire energy range, obtaining a measurement of the shape versus the neutron energy of the ratio accurate to ±2% over most of the energy range. Two independent methods determined the normalization of the shape measurement.