Monte Carlo computer simulations were performed under thermodynamic conditions corresponding to available X-ray and neutron diffraction measurements of the supercritical water structure. A detailed analysis of hydrogen bonding in supercritical water is presented, based on the recently proposed hybrid distance-energy criterion of H-bonding. Good agreement is found with all available experimental and computer simulated results. With increasing temperature, the average number of H-bonds per a water molecule, [n(HB)], decreases with the same slope for both high-density (similar to 1.0 g/cm(3)) as well as low-density (similar to 0.2 g/cm(3)) supercritical water, asymptotically approaching zero at higher temperatures and lower densities. Over the whole supercritical region, except fur the highest density slates, [n(HB)] is always below the percolation threshold (similar to 1.6), indicating that the continuous network of hydrogen bonds is broken. Nevertheless, even at the highest temperature and the lowest density simulated, some degree of hydrogen bonding is still present in the form of dimers and trimers. For supercritical conditions of 673 R and 0.66 g/cm(3), average hydrogen bonds are almost 10% weaker, 5% longer, and about 8 degrees more bent, compared to those in normal liquid water. However, over 40% of them are still preserved in the supercritical state, in good aggreement with estimates from all available experimental data.