The fission decay probabilities of the 235Pa and 236U compound nuclei produced in a single experiment in ²³²Th(7Li, αf )²³⁵Pa and ²³²Th(⁷Li, tf )²³⁶U transfer induced fission reaction channels, have been measured at E_lab = 39.5 MeV in the excitation energy range of 14–20 MeV. The ²³⁴Pa(n, f) cross sections are then deduced from the measured fission decay probability ratios of ²³⁵Pa and ²³⁶U compound systems in the equivalent neutron energy range of 8–14 MeV within the framework of the hybrid surrogate ratio method, considering the well-measured ²³⁵U(n, f) cross sections as the reference. The experimental data on ²³⁴Pa(n, f) cross sections have been compared with the calculated fission cross sections using EMPIRE-3.1 code with the fission barrier height values obtained from barrier formula (BF) as well as RIPL-3 [24]. The present experimental results are found to be in very good agreement with the EMPIRE-3.1 predictions for the fission barrier heights predicted by the BF.