  Individual gamma ray bursts (GRBs) have very diverse time behavior - from a
single pulse to a long complex sequence of chaotic pulses of different
timescales. I studied light curves of GRBs using data from the CGRO's BATSE
experiment and found that the average post-peak time history for a sample of
460 bursts obeys an unique and simple analytical law: $I \sim
\exp(-(t/t_0)^{1/3})$ where $t$ is time measured from the peak of the event and
$t_0$ is a constant ranging from 0.3 sec for strong bursts to $\sim 1$ sec for
weak bursts. The average peak aligned profile follows this law with good
accuracy in the whole range availible for analysis (from fractions of a second
to $\sim$ 150 seconds after the peak). Such a law with a single time constant
characterising the overall sample of GRBs should have important physical
meaning. The dependence of $t_0$ versus brightness of GRBs is presented. The
fact that $t_0$ depends on the brightness apparantly confirms the recently
discovered effect of time dilation of weak bursts which has a possible
cosmological interpretation. The time dilation is detected at a confidence
level of $7\sigma$ and it is slightly larger than was previously reported.
