Synoptic maps of Ca II K-normalized intensity at +/- 40 degrees latitude belt from Carrington rotations 827 (1915 August 10) to 1764 (1985 July 7) are utilized to investigate the long-term variation of the quiet chromospheric differential rotation within solar activity cycles through removing some large values of Ca II-normalized intensity. The equatorial rotation rate of the quiet chromosphere is found to be smaller than that of the chromosphere, and the absolute value of the parameter B is also found to be smaller for the quiet chromosphere than for the chromosphere on the whole, especially during periods of solar cycle maxima. Therefore, we induce that the differential of rotation rate in the quiet chromosphere seems to be enhanced by large-scale magnetic fields. The north-south asymmetry in the solar rotation is also investigated, and the asymmetry coefficients of the chromosphere and the quiet chromosphere are positively correlated in solar cycles 15-17, while they are negatively correlated in solar cycles 18-21.