The latitudinal variation of sunspots appearing during the period from 1874 to 2009 has been studied in terms of centerof-latitude (COL). The butterfly diagram has been used to study the evolution of the magnetic field and the dynamics at the bottom of the solar convection zone. Short-term periodicities have been of particular interest, in that they are somehow related to the structure and dynamics of the solar interior. We thus have focused our investigation on shortterm periodicities. We first calculated COL by averaging the latitude of sunspots with the weight function in area. Then, we analyzed the time series of COL using the wavelet transform technique. We found that a periodicity of ~5 years is the most dominant feature in the time series of COL, with the exception of the ~11 year solar cycle itself. This periodicity can be easily understood by considering small humps between the minima in the area-weighted butterfly diagram. However, we find that periodicities of ~1.3 (0.064), ~1.5 (0.056), or ~1.8 (0.046) years ($frac{1}{month}$), month ), which have been previously suggested as evidence of links between the changing structure of the sunspot zone and the tachocline rotation rate oscillations, are insignificant and inconsistent. We therefore conclude that the only existing short-term periodicity is of ~5 years, and that periodicities of ~1.3, ~1.5, or ~1.8 years are likely to be artifacts due to random noise of small sunspots.