We carefully analysis the spectral properties of the 17 well-known mapped PG QSOs, in order to find more reliable dependence of the spectra index on the continuum luminosity, i.e., the common sense "AGNs get bluer when they get brighter". However, we can finally confirm that there are no strong correlation between the spectral index and the continuum luminosity  (correlation coefficient less than 0.5), and moreover we can confirm that there are much different intrinsic variability modes for the spectral index and for the continuum emission by the Damped Random Walk method. Therefore, we  commonly accepted common sense "AGNs get bluer when they get brighter" is not so common as what we have expected. 

By with ZHANG XueGuang  

 DRW fitted results for the variabilities of the spectral index and the continuum emission. The solid blue circles plus error bars are the observed data values and the corresponding uncertainties. The red solid line and red dotted lines are the best DRW descriptions for the variabilities and the corresponding $1\sigma$ variance range respectively. The research work by XueGuang Zhang has been accepted and to be published in MNRAS (http://mnras.oxfordjournals.org/content/early/2013/09/04/mnras.stt1432.full)