  The new analysis variable xi, shown to be powerful on the data taken with the
final configuration of CELESTE, has been applied to data taken with previous
detector configurations. First, the analysis is validated on Crab observations,
and then the cuts for the blazar Mrk 501 are optimized using Mrk 421 data since
the sources have similar declinations. Data from Mrk 501 was recorded in 2000
and 2001. The old analysis gave a 2.5 sigma excess. We obtain an excess of 2.9
sigma during this time and of 4.9 sigma during May and June 2000 that we
interpret as a gamma-ray signal from Mrk 501, for which we calculate a flux of
(6.9 +/- 2.2) * 10^{-7} photons m^{-2} s^{-1}. An upper limit from the other
data with no signal is determined.
