The general theory on the biological foundations of cerebral dominance formulated in 1985 by Geschwind and Galaburda entirely relies on a postulated causal relationship between anatomical asymmetry of the planum temporale and functional lateralization of the human brain, but does not take into account asymmetry of another cortical region, the parietal operculum. In 40 normal volunteers whose handedness was specified by the Edinburgh Handedness Inventory, we assessed asymmetries of these two regions on MRI sagittal scans. For both measurements, a significantly larger leftward asymmetry was found in the 24 consistent right-handers compared to the 16 non-right-handers. Moreover, the combination, for each subject, of the two indices of asymmetry, yielded four different subtypes between which handedness distribution significantly differed. We conclude that planum temporale and parietal operculum asymmetries may be divergent and that their convergence is strongly associated with right-handedness. Functional and developmental implications of these findings are discussed by reference to the Geschwind/Galaburda theory.