We obtain a tighter bound on the probability of making a correct selec tion in Paulson's procedure for selecting the normal population which has the largest population mean when the populations have a common unknown Tali ance. As a consequence, we are able to use a sharper value for the coristallt a*in Paulson's procedure. Simulation studies indicate that this leads to ari inlprovement in the expected number of stages to termination and expettetl total number of observations which is uniform in k, P*s and σ/δ*.