Fission fragment mass distribution has been measured for ²⁸Si + ¹⁹⁷Au reaction at bombarding energies around the Coulomb barrier (V_b = 126.5MeV). The experimental variance of the mass distribution shows a sudden change from monotonic decrease to a saturation at energies close to the Coulomb barrier and again a decreasing trend at sub-barrier energies. The variance of the mass distribution was also obtained from dynamical and statistical model calculations for the fission of a fully equilibrated compound nucleus. Both of the theoretical calculations show a monotonic change of the mass variance around the Coulomb barrier. The anomalous dependence of fission fragment mass width at energies around the barrier may be due to the dominance of the quasifission process as compared to compound nuclear fission.