We use the NASA-JPL global ionospheric maps of total electron content (TEC), obtained from observations of GPS satellite signals, to construct average noon TEC maps for one-month periods centered on the June and December solstices of 2002. By combining data from equivalent points in the northern and southern hemispheres, we find that the combined north+south TEC in December substantially exceeds that in June, almost everywhere. The global average of an ‘Asymmetry Index’ (AI) used to characterize such patterns, AI=(Dec−June)/(Dec+June), results in AI=0.15 for 2002, far greater than the value of 0.035 that corresponds to the annual variation of the solar irradiance due to Sun-Earth distance. Since the F2-layer makes the major contribution to TEC, we regard this as a manifestation of the F2-layer annual asymmetry, discovered some decades ago but never explained. The neutral atomic oxygen/molecular nitrogen concentration ratio, derived from the GUVI experiment on the TIMED satellite, shows a similar but smaller asymmetry (AI=0.06), providing some evidence that the ionospheric asymmetry is related to changes in thermospheric composition, with a still smaller AI=0.03 in the NRL MSIS thermospheric model.