A method for determining the quadrupole deformation parameter of transuranium nuclei is presented. This method is based on giant dipole resonance splitting in the photofission cross section. The experimental setup containing an avalanche counter of fission fragments, as well as a method for reconstructing the cross section from the measured dependence of the photofission reaction yield on the endpoint energy of the bremsstrahlung spectrum, are described. The setup was tested on the bremsstrahlung beam of the MT-25 microtron at the Flerov Laboratory for Nuclear Reactions of the Joint Institute for Nuclear Research. The test results—in particular, the measured excitation function of the uranium photofission reaction—are presented.