  We present a new calculation of the intergalactic $\gamma$-ray
pair-production absorption coefficient as a function of both energy and
redshift up to the redshift of 3C279, z = 0.54. In reexamining this problem, we
make use of new observational data on the intergalactic infrared radiation
field (IIRF), together with recent theoretical models of the galactic spectral
energy distributions of the IIRF from stars and dust reradiation and estimates
of the IIRF from galaxy counts and {\it COBE} results. We present our results
for two fairly well defined IIRF spectral energy distributions, one of which is
within $1 \sigma $ of our previous estimate of the IIRF at $ \sim 20$ $\mu$m.
We then apply our results to the $\gamma$-ray spectrum of Mrk 421, and obtain
good agreement with the observational data, including the recent results of the
{\it HEGRA} group.
