Temporal variation of the solar coronal rotation appears to be very complex and its relevances to the eleven-year solar activity cycle are still unclear . Using the modified coronal index for the time interval from 1939 January 1 to 2019 May 31 , the systematic regularities of the solar coronal rotation are investigated . Our main findings are as follows : ( 1 ) from a global point of view , the synodic coronal rotation period with a value of 27.5 days is the only significant period at the periodic scales shorter than 64 days ; ( 2 ) the coronal rotation period exhibit an obviously decreasing trend during the considered time interval , implying the solar corona accelerates its global rotation rate in the long run ; ( 3 ) there exist significant periods of 3.25 , 6.13 , 9.53 , and 11.13 years in the period length of the coronal rotation , providing an evidence that the coronal rotation should be connected with the quasi-biennial oscillation , the eleven-year solar cycle , and the 22-year Hale cycle ( or the magnetic activity reversal ) ; and ( 4 ) the phase relationship between the coronal rotation period and the solar magnetic activity is not only time-dependent but also frequency-dependent . For a small range around the 11- year cycle band , there is a systematic trend in the phase , and the small mismatch in this band brings out the phase to drift . The possible mechanism for the above analysis results is discussed .