We use a continuous wavelet transform to analyse the daily hemispheric sunspot area data from the Greenwich Royal Observatory during cycles 12-24 and then study the cause of the appearance or disappearance of the Rieger-type periodicity in the northern and southern hemispheres during a certain cycle. The Rieger-type periodicity in the northern and southern hemispheres should be developed independently in the two hemispheres. This periodicity in the northern hemisphere is generally anti-correlated with the long-term variations in the mean solar cycle strength of hemispheric activity, but the correlation of the two parameters in the southern hemisphere shows a weak correlation. The appearance or disappearance of Rieger-type periodicity in the northern and southern hemispheres during a certain solar cycle is not directly correlated with their corresponding hemispheric mean activity strength but should be related to the strength of the hemispheric activity during sunspot maximum times, which hints the Rieger-type periodicity is more related to temporal evolution of toroidal magnetic field. The Rieger-type periodicity in the two hemispheres disappears in those solar cycles with relatively weak hemispheric activity during sunspot maximum times. The reason for the disappearance of this periodicity may be due to the combined influence of relatively weak toroidal magnetic fields and torsional oscillations, the differential rotation parameters vary through the solar cycle and may not remain more or less unchanged during some time, which does not permit the strong growth of magnetic Rossby waves.