  We test the correlation found by Reichart et al. (2001) between time
variability and peak luminosity of Gamma-Ray Bursts (GRBs). Recently Guidorzi
et al. (2005) found that this still holds for a sample of 32 GRBs with
spectroscopic redshift, although with a larger scatter than that originally
found by Reichart et al. (2001). However Guidorzi et al. (2005) also found that
a power law does not provide a good description of that. We report on the same
test performed on a sample of 551 BATSE GRBs with a significant measure of
variability assuming the pseudo-redshifts derived by Band et al. (2004) (1186
GRBs) through the anticorrelation between spectral lag and peak luminosity. We
still find a correlation between variability as defined by Reichart et al.
(2001) and peak luminosity with higher significance. However, this subsample of
BATSE GRBs show a higher scatter around the best-fitting power law than that
found by Reichart et al. (2001) in the variability/peak luminosity space. This
is in agreement with the result found by Guidorzi et al. (2005) on a sample of
32 GRBs with measured redshift. These results confirm that a power law does not
provide a satisfactory description for all the GRBs, in contrast with the
original findings by Reichart et al. (2001).
