Abstract
We present the gamma-ray spectrum of the BL Lacertae object, Markarian 421, above 500 GeV during its most intense recorded TeV flare, on 1996 May 7. The spectrum is well fitted by a power law with an exponent of -2.56±0.07±0.1 (statistical and systematic errors). The spectrum extends above 5 TeV with no evidence for a cutoff, favoring determinations of the extragalactic infrared energy density that do not produce a sharp cutoff at these energies.