  Routine observations of the Crab Nebula for a total of about 250 hrs,
performed with the HEGRA stereoscopic system of 5 imaging atmospheric Cerenkov
telescopes in the standard operational mode, have proven the energy threshold
of the system to be 500 GeV for small zenith angles (< 20 deg). A topological
trigger applied along with the convergent observational mode allows to reduce
noticeably the energy threshold of the system down to 350 GeV. Here we present
the relevant Monte Carlo simulations as well as the analysis results of 15 hrs
Crab Nebula data taken in such an observational mode. From the Crab Nebula
data, the final energy threshold was found to be 350 GeV. The estimated gamma
ray flux from the Crab Nebula above 350 GeV is (8.1 +- 0.1(stat) +- 0.2(syst))
10^(-11) ph cm^(-2) s^(-1), which is consistent with recent measurements
reported by the STACEE, CELESTE, CAT, and Whipple groups.
