  It is largely recognized that Gamma-Ray Burst (GRB) jets involve
ultra-relativistic motion. However, the value of the Lorentz factor Gamma_0 is
still not clear and only lower limits are known for most bursts. We suggest
here a new method to obtain upper limits on Gamma_0. The early high-energy
synchrotron afterglow flux depends strongly on Gamma_0. Upper limits on GeV
emission therefore provide uppers limit on Gamma_0. Applying this method to 190
Fermi GRBs that have not been detected by the Fermi-LAT we place upper limits
on the high-energy afterglow flux, and in turn on Gamma_0. For bursts at a
typical redshift z=2, we find values of the order of 200 (and above) for a
homogeneous density medium, and in the range 100-400 for a wind-like medium.
These upper limits are consistent with (and are very close to) lower limits and
direct estimates inferred using other methods, suggesting that the typical
Lorentz factors of GRB jets are of order a few hundred.
