The Hall conductivity sigma_{xy} of Dirac electrons with a spin-orbit interaction is examined. It is shown that there is an unconventional contribution to sigma_{xy} generated by the interband effects of a magnetic field, which is remarkable near the band edges and does not depend on impurity scatterings so much, suggesting the same origin as the known large diamagnetism. Correspondingly, the Hall coefficient exhibits unexpected peaks at around the band edges. Implications of the present results to bismuth alloys are discussed.