The evolution of haemagglutinin (HA), an important influenza virus antigen, has been the subject of intensive research for more than two decades. Many characteristics of HA's sequence evolution are captured by standard Markov chain substitution models. Such models assign equal fitness to all accessible amino acids at a site. We show, however, that such models strongly underestimate the number of homoplastic amino acid substitutions during the course of HA's evolution, i.e. substitutions that repeatedly give rise to the same amino acid at a site. We develop statistics to detect individual homoplastic events and find that they preferentially occur at positively selected epitopic sites. Our results suggest that the evolution of the influenza A HA, including evolution by positive selection, is strongly affected by the long-term site-specific preferences for individual amino acids.