  Rotation is a significant characteristic of the Sun and other stars, and it
plays an important role in understanding their dynamo actions and magnetic
activities. In this study, the rotation of the solar chromospheric activity is
investigated from a global point of view with an over 40 yr Mg II index. We
determined the time-varying rotational period lengths (RPLs) with the
synchrosqueezed wavelet transform which provides high temporal and frequency
resolution; furthermore, we compared the RPLs with the photospheric and coronal
RPLs obtained from the sunspot numbers and the 10.7 cm radio flux data. The
significance of the RPLs is taken into consideration. We found that the RPLs of
the chromosphere exhibit a downward trend, as do those that of the photosphere
and corona; in addition, their RPLs at the recent four solar maxima also show a
declining trend. It suggests that the rotation of the solar atmosphere has been
accelerating during the recent four solar cycles, which is inferred to be
caused by the declining strength of solar activity. The variations of the solar
atmospheric RPLs show periodicities of multiple harmonics of the solar cycle
period, and it is modulated by the solar activity cycle.
