Observations (Espey et al. 1989, Carswell et al. 1991, Marziani et al. 1996) at high resolution have shown relative shifts between the Balmer lines and the C iv line in a number of QSOs. In this paper, we suggest that in the BLR there are many cloudlets with dense gas that is optically thick, and the BLR is not only illuminated by UV-X radiation, but also by relativistic electrons. Therefore the Čerenkov line radiation has to be taken into consideration, and we calculate the Čerenkov line redshifts and the profiles.