The HA1 domain of HA, the major antigenic protein of influenza A viruses, contains all of the antigenic sites of HA and is under continual immune-driven selection. To resolve controversies on whether only a few or many residue sites of HA1 have undergone positive selection, whether positive selection at HA1 is continual or punctuated, and whether antigenic change is punctuated, we introduce an approach to analyze 2,248 HA1 sequences collected from 1968 to 2005. We identify 95 substitutions at 63 sites from 1968 to 2005 and show that each substitution occurred very rapidly. The rapid substitution and the fact that 57 of the 63 sites are antigenic sites indicate that hitchhiking plays a minor role and that most of these sites, many more than previously found, have undergone positive selection. Strikingly, 88 of the 95 substitutions occurred in groups, and multiple mutations at antigenic sites sped up the fixation process. Our results suggest that positive selection has been ongoing most of the time, not sporadic, and that multiple mutations at antigenic sites cumulatively enhance antigenic drift, indicating that antigenic change is less punctuated than recently proposed.