The fission probability of 234,236U as a function of the excitation energy has been measured with high energy resolution using the 233,235U(d, pf) reactions in order to study hyperdeformed (HD) rotational bands. Rotational band structures with a moment of inertia of = 238 ± 42 2/MeV and = 217 ± 38 2/MeV have been observed for 234,236U, respectively, corresponding to hyperdeformed configurations. From the level density of the rotational bands the excitation energy of the ground state in the third minimum was determined to be E III = 3.1 ± 0.4 MeV and EIII = 2.7 ± 0.4 MeV, for 234U and for 236U, respectively. The excitation energy of the lowest hyperdeformed transmission resonance and the energy dependence of the fission isomer population probability enabled the determination of the height of the inner fission barrier of 236U EA = 5.15±0.20 MeV and its curvature parameter ωA=1.2 MeV. Using this new method the long-standing uncertainties in determining the height of the inner potential barrier in uranium isotopes could be resolved.