We present the gamma-ray spectrum of the BL Lacertae object, Markarian
421, above 500 GeV during its most intense recorded TeV flare, on 199
6 May 7. The spectrum is well fitted by a power law with an exponent o
f -2.56 +/- 0.07 +/- 0.1 (statistical and systematic errors). The spec
trum extends above 5 TeV with no evidence for a cutoff, favoring deter
minations of the extragalactic infrared energy density that do not pro
duce a sharp cutoff at these energies.