The fast luminosity monitor counting the γ photons above a given energy threshold emitted from radiative Bhabha scattering has been operated in the BEPCII to measure the relative luminosity bunch by bunch for the first time and used successfully in beam tuning of BEPCII. In the relative mode the monitor is able to deliver the relative luminosities with an accuracy of 0.8%. By steering the electron beam while observing the counting rate changes of the monitor the horizontal and vertical sizes of the bunch spots can be estimated as: sxe+ = sxe– = 0.356 mm, sye+ = sye– = 0.011 mm.