Abstract Global solar activity variation mainly occurs over about an 11 yr cycle. However, both longer and shorter periodicities than the solar cycle are also present in many different solar activity indices. The longer timescales may be up to hundreds of years, while the shorter timescales for global solar variability could be within 0.5–2 yr, which include, e.g., from the Rieger-type periods (150–160 days) to quasi-biennial oscillations of 2 yr. The most likely origin of this short-timescale quasi-periodicity is attributed to magnetic Rossby waves, which have periods of 0.8–2.4 yr. In this work, we present findings of a unique evolution of identified shorter periodicities, like the Rieger-type, arising from magnetic Rossby waves, throughout Solar Cycles 19–25. We report further observational evidence of the strong relationship between the Rieger-type periodicity, magneto-Rossby waves, and major solar flare activity. Moreover, this study also reveals that the global solar magnetic field has a continuous periodic longitudinal conveyor belt motion along the solar equator, together with an up-and-down movement in the latitudinal directions. We found that when these longitudinal and latitudinal movements have Rieger-type periodicity and magneto-Rossby waves during the same period of a solar cycle, major flare activity is present.