In this study, we calculate the unpredictable portion of amino-acid pairs, which has been developed by us over the last several years, of 1201 hemagglutinins from influenza A viruses dated from 1918 to 2004 in order to compare them with respect to subtypes, species, and years. After noticing the fluctuations of unpredictable portion along the time course, we use the fast Fourier transform to find the mutation periodicity of hemagglutinins. Then we estimate our position at the current cycle of hemagglutinin evolutionary process to determine how many years remain before the next outbreak of influenza and bird flu. Finally, we use the trend line and channel to outlook the hemagglutinins for the next half a century. As our study covers almost all the full-length amino-acid sequences of hemagglutinins from various influenza A viruses, the conclusion will be valid for years until the number of hemagglutinins in protein databank will be significantly increased. (c) 2005 Elsevier Inc. All rights reserved.