Mkn~421 was observed during a high flux state for nine nights in April and May 2004 with the fully operational High Energy Stereoscopic System ( H.E.S.S . )
in Namibia .
The observations were carried out at zenith angles of 60 ^ { \circ } –65 ^ { \circ } , which result in an average energy threshold of 1.5 TeV and a collection area reaching 2 km ^ { 2 } at 10 TeV .
Roughly 7000 photons from Mkn 421 were accumulated with an average gamma-ray rate of 8 photons/min .
The overall significance of the detection exceeds 100 standard deviations .
The light-curve of integrated fluxes above 2 TeV shows changes of the diurnal flux up to a factor of 4.3 .
For nights of high flux , intra-night variability is detected with a decay time of less than 1 hour .
The time averaged energy spectrum is curved and is well described by a power-law with a photon index \Gamma = 2.1 \pm 0.1 _ { \mathrm { stat } } \pm 0.3 _ { \mathrm { sys } } and an exponential cutoff at E _ { c } = 3.1 ( +0.5 -0.4 ) _ { \mathrm { stat } } \pm 0.9 _ { \mathrm { sys } } TeV and an average integral flux above 2 TeV of 3 Crab flux units .
Significant variations of the spectral shape are detected with a spectral hardening as the flux increases .
Contemporaneous multi-wavelength observations at lower energies ( X-rays and gamma-rays above \approx 300 GeV ) indicate smaller relative variability amplitudes than seen above 2 TeV during high flux state observed in April 2004 .