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Since FRB 200428 has been found to be associated with an X-ray burst from the Galactic magnetar SGR J1935+2154, it is interesting to explore whether the magnetar bursts also follow the similar active periodic behavior as some repeating FRBs. Previous studies show that there is possible period about 230 day in SGR J1935+2154 bursts. Here, we collected an updated burst sample from SGR J1935+2154, including all bursts reported by Fermi/GBM and GECAM till 2022 January. We also developed a targeted search pipeline to reveal more bursts from SGR J1935+2154 in the Fermi/GBM data from 2008 August to 2014 December (i.e. before the first burst detected by Swift/BAT). With this burst sample, we re-analyzed the possible periodicity of SGR J1935+2154 bursts using the Period Folding and Lomb-Scargle Periodogram methods. Our results show that the periodicity $\sim$238 day reported in literature is probably fake and the observation effects may introduce false periods (i.e. 55 day) according to simulation tests. We find that, for the current burst sample, the most probable period is 126.88$\pm$2.05 day, which could be interpreted as the precession of the magnetar. However, we note that the whole burst history is very complicated and difficult to be perfectly accommodated with any period reported thus far, therefore more monitoring observations of SGR J1935+2154 are required to test any periodicity hypothesis.