The ocurrence times of major flares of solar cycle 22 are analyzed to detect periodicities. It is found that a periodicity of 77 d was in operation in the 15-m interval from 1988 November to 1990 February for six cycles. During the rest of 1990 no periodicity was discernible; however, it seems that the 77-d periodicity resumed in 1991. This 77-d period is interpreted as the third subharmonic of the fundamental period of about 25.5 d. In this interpretation, the 154-d periodicity is the sixth subharmonic. It is also found that when the 77-d periodicity or the 154-d periodicity is in operation the occurrence rate of major flares is much higher than is expected form the relative sunspot number.