Abstract: The potential energy curves of the ground state X²∑⁺_g of the fluorine molecule have been ac-curately reconstructed employing the Ryderg-Klein-Rees (RKR) method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the cor-responding radial one-dimensional Schr?dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimen-tal data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm?1 and the relative de-viation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F₂ ground state.