  The HEGRA system of imaging air Cherenkov telescopes has been used to observe
the BL Lac object H1426+428 ($z=0.129$) for 217.5 hours in 2002. In this data
set alone, the source is detected at a confidence level of $5.3~\sigma$,
confirming this object as a TeV source. The overall flux level during the
observations in 2002 is found to be a factor of $\approx 2.5$ lower than during
the previous observations by HEGRA in 1999&2000. A new spectral analysis has
been carried out, improving the signal-to-noise ratio at the expense of a
slightly increased systematic uncertainty and reducing the relative energy
resolution to $\Delta E/E\le 12 %$ over a wide range of energies. The new
method has also been applied to the previously published data set taken in 1999
and 2000, confirming the earlier claim of a flattening of the energy spectrum
between 1 and 5 TeV. The data set taken in 2002 shows again a signal at
energies above 1 TeV. We combine the energy spectra as determined by the CAT
and VERITAS groups with our reanalyzed result of the 1999&2000 data set and
apply a correction to account for effects of absorption of high energy photons
on extragalactic background light in the optical to mid infrared band. The
shape of the inferred source spectrum is mostly sensitive to the
characteristics of the extragalactic background light between wavelengths of 1
and 15~$\mu$m
