There are extremely luminous quasi stellar objects (QSOs) at high redshift which are absent at low redshift.The lower luminosities at low redshifts can be understood as the external manifestation of either a lower Eddington ratio or a lower mass.To distinguish between both effects,we determine the possible dependence of masses and Eddington ratios of QSOs with a fixed luminosity as a function of redshifts; this avoids the Malmquist bias or any other selection effect.For the masses and Eddington ratios derived for a sample of QSOs in the Sloan Digital Sky Survey,we model their evolution by a double linear fit separating the dependence on redshifts and luminosities.The validity of the fits and possible systematic effects were tested by the use of different estimators of masses or bolometric luminosities,and possible intergalactic extinction effects.The results do not show any significant evolution of black hole masses or Eddington ratios for equal luminosity QSOs.The black hole mass only depends on the bolometric luminosity without significant dependence on the redshift as (MBH/109M☉)≈ 3.4 (Lbol/(1047ergs-1)0.65on average for z ≤ 5.This must not be confused with the possible evolution in the formation of black holes in QSOs.The variations of the environment might influence the formation of the black holes but not their subsequent accretion.It also leaves a question to be solved:Why are there not QSOs with very high mass at low redshift? A brief discussion of the possible reasons for this is tentatively pointed out.