  The region around PSR B1706-44 has been observed with the H.E.S.S. imaging
atmospheric Cherenkov telescopes in 2003. No evidence for gamma-ray emission in
the TeV range was found at the pulsar position or at the radio arc which
corresponds to the supernova remnant G 343.1-2.3. The 99% confidence level flux
upper limit at the pulsar position is Ful(E > 350GeV) = 1.4e-12 /cm^2/s
assuming a power law with photon index of 2.5 and Ful(E > 500GeV) = 1.3e-12
/cm^2/s without an assumption on the spectral shape. The reported upper limits
correspond to 8% of the flux from an earlier detection by the CANGAROO
experiment.
