The occurrence frequency of the largest geomagnetic storms from 1868--1998 exhibits a well-defined semiannual modulation with more than twice as many storms occurring during equinoctial months than at the solstices. To examine the cause of this seasonal imbalance, we empirically obtained a new geomagnetic index aam that has the same seasonal and Universal Time variation as the am index. In effect, this extends the am index backward in time to 1868. By normalizing the aam time series for Ψ, the angle between the solar wind flow direction and Earth's dipole, we removed 75% of the amplitude of the six-month wave in monthly averages of aam and ~75% of the seasonal discrepancy in the numbers of great storms. We obtained similar percentages for the (unmodified) am index over the shorter 1959--1998 interval. These results indicate that most, though not all, of the discrepancy in storm counts between the equinoxes and solstices is due to an equinoctial effect.