Hemispheric asymmetry of solar magnetic structures is an important feature of solar cycles, and it involves dynamical processes in the interior of the Sun. For the first time, the data of the monthly sunspot relative numbers derived from the National Astronomical Observatory of Japan (NAOJ) is used to perform a long-term study (1939 March-2019 November) of the north-south asymmetry. The results show the following: (1) the sunspot relative numbers derived from NAOJ/Mitaka observatory are highly correlated with the international sunspot numbers obtained from the World Data Center Sunspot Index and Long-term Solar Observations, which justifies the use of Mitaka sunspot time series for hemispheric variation; (2) the change in the signs of the slopes of the regression lines fitted to the absolute asymmetry index suggest a kind of periodic variation in the hemispheric asymmetry, but the time interval of the current data base is not long enough to derive 8 or 12 cycles periodicity; and (3) for mid-term periods, there are enhanced powers for the period ranges around 3.7 yr, around 9 yr, between 30 and 50 yr. Our analysis results implicate a possible mechanism responsible for the generation and variation of the hemispheric coupling in the Sun.