Coronal heating is a big question for modern astronomy. Daily measurement of 985 solar spectral irradiances (SSIs) at the spectral intervals 1-39 and 116-2416 nm during 2003 March 1 to 2017 October 28 is utilized to investigate characteristics of solar rotation in the solar atmosphere by means of the Lomb-Scargle periodogram method to calculate their power spectra. The rotation period of coronal plasma is determined to be 26.3 days, and that of the solar atmosphere at the bottom of the photosphere modulated by magnetic structures is 27.5 days. Here we report for the first time that, unexpectedly, the coronal atmosphere is found to rotate faster than the underlying photosphere. When time series of SSIs are divided into different cycles as well as the ascending and descending periods of a solar cycle, the rotation rate in the corona is also found to be larger than that in the photosphere, and this actually uncovers hidden evidence: it is small-scale magnetic activity that heats the corona.