  We present a new calculation of the intergalactic gamma-ray absorption
coefficient as a function of both energy and redshift. In reexamining this
problem, we make use of a new, empirically based calculation (as opposed to
previous model calculations) of the intergalactic infrared radiation field. We
find smaller opacities than those given previously (Stecker & De Jager 1997).
We apply our results to the new observations of the flaring gamma-ray spectra
of Mrk421 and Mrk501, both at a redshift of apx. 0.03. Our new calculations
indicate that there should be no significant curvature in the spectra of these
sources for energies below 10 TeV, as indicated by recent observations.
However, the intrinsic spectra of these sources should be harder by apx. 0.2 to
0.45 in the spectral index in the 1 to 10 TeV range with an intergalactic
absorption cutoff above apx. 20 TeV.
