Using recently measured accurate relative partial ionization cross section functions for production of the C-60 fragment ions C-58(+) through C-44(+) by electron impact ionization, we have determined the respective binding energies BE(C-n(+)-C-2), with n = 58,...,44, using a novel self-consistent procedure. Appearance energies were determined from ionization efficiency curves. Binding energies were calculated from the corresponding appearance energies with the help of the finite heat bath theory. Then using these binding energies we calculated with transition state theory (TST), the corresponding breakdown curves, and compared these calculated ones with the ones derived from the measured cross sections. The good agreement between these breakdown curves proves the consistency of this multistep calculation scheme. As the only free parameter in this procedure is the binding energy C-58(+)-C-2, we studied the influence of different transition states chosen in the determination of this binding energy via TST theory and iterative comparison with breakdown curve measurements, Based on this study we can conclude that extremely loose transition states can be confidently excluded, and that somewhat looser transition states than those used earlier result in an upward change of the binding energy of less than 10% yielding an upper limit for the binding energy C-58(+)-C-2 of approximately 7.6 eV.