Solar-cycle related variation of differential rotation is investigated through analyzing the rotation rates of magnetic fields, distributed along latitudes and varying with time at the time interval of August 1976 to April 2008. More pronounced differentiation of rotation rates is found to appear at the ascending part of a Schwabe cycle than at the descending part on an average. The coefficient $B$ in the standard form of differential rotation, which represents the latitudinal gradient of rotation, may be divided into three parts within a Schwabe cycle. Part one spans from the start to the $4^{th}$ year of a Schwabe cycle, within which the absolute $B$ is approximately a constant or slightly fluctuates. Part two spans from the $4^{th}$ to the $7^{th}$ year, within which the absolute $B$ decreases. Part three spans from the $7^{th}$ year to the end, within which the absolute $B$ increases. Strong magnetic fields repress differentiation of rotation rates, so that rotation rates show less pronounced differentiation, but weak magnetic fields seem to just reflect differentiation of rotation rates. The solar-cycle related variation of solar differential rotation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation of rotation rates.

19 pages, 8 figures, accepted by MNRAS. arXiv admin note: text overlap with arXiv:1305.3970