  Data taken with the HEGRA system of imaging atmospheric Cherenkov telescopes
during the 1997 flares of Mkn 501 are reanalyzed using an algorithm providing
improved energy resolution. A resolution of 10% to 12% is obtained by
accounting for the variation of the Cherenkov light yield with the height of
the shower maximum in the atmosphere. The improved energy resolution is
particularly relevant for the study of the high-energy cutoff in the spectrum,
which might be caused by interactions with the intergalactic infrared
background radiation. The reanalysis presented here confirms the results
obtained in the previous analysis, but hints a steeper slope of the spectrum in
the region around 20 TeV.
