The observations of the active galactic nucleus Markarian 501 were conducted at the Crimean Astrophysical Observatory with the GT-48 ground-based atmospheric Cherenkov detector in May and June 1997. The data were proccessed using multidimensional analysis. The very high energy -ray flux was detected at a highly significant level of 19.1 standard deviation. The integral flux value above 0.9 TeV averaged over the observational period amounted to (5.6±0.3±0.5) × 10^-11 cm^-2 s^-1 . Here the second and the third terms stand for statistical and systematic errors, respectively. This result is in good agreement with the Whipple and the CAT observational data.