  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.
