The photofission yields of Bi, Pb, Au, Pt, Re, W and Ta have been measured by using a bremsstrahlung photon beam at maximum energies from 300 MeV to 1000 MeV. The fission fragments have been detected by means of glass sandwiches. The behaviour of the photofission cross-section has been deduced by applying an appropriate unfolding method to the results of the present experiment and to the data of previous measurements performed by a coherent photon beam. The cross-sections obtained for all the seven studied elements clearly show a first resonance at a photon energy k ≃ 340 keV and a second one centred at k ≃ 720 MeV, in good agreement with the position of the baryon resonances in the pion photoproduction. The resonant behaviour of the photofission cross-section is explained by assuming a photomesonic model of the photofission process and a nuclear fissility increasing with photon energy