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The full-disk chromosphere was routinely monitored in the He I 10830\AA\,line at the National Solar Observatory/Kitt Peak from 2004 Nov. to 2013 March,and thereby, synoptic maps of He I line intensity from Carrington rotations2032 to 2135 were acquired. They are utilized to investigate the differentialrotation of the chromosphere and the quiet chromosphere during the one falling(descending part of solar cycle 23) and the one rising (ascending part of solarcycle 24) period of a solar cycle. Both the quiet chromosphere and thechromosphere are found to rotate slower and have a more prominent differentialrotation, in the rising period of solar cycle 24 than in the falling period ofsolar cycle 23, and an illustration is offered.

The differential rotation of the chromosphere and the quiet chromosphere in the falling and rising period of a solar cycle