We present preliminary results of an off-line search for non-triggered gamm
a-ray bursts (GRBs) in the BATSE daily records for about 5.7 years of obser
vations. We found more GRB-like events than the yield of the similar search
of Kommers et al. (1998) and extended the log N - log P distribution down
to - 0.1 ph cm(-2) s(-1). The indication of a turnover of the log N - log P
at a small P is not confirmed: the distribution is straight at 1.5 decades
with the power law index -.6 and cannot be fitted with a standard candle c
osmological model.