Data taken with the HEGRA system of imaging atmospheric Cherenkov telescope
s during the 1997 flares of Markarian 501 (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 w
ith the height of the shower maximum in the atmosphere. The improved energy
resolution is particularly relevant for the study of the high-energy cutof
f in the spectrum, which might be caused by interactions with the intergala
ctic 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.