A method of catalytically decomposing water, which comprises contacting water with a composite catalyst comprising a solid acid catalyst and a solid base catalyst at an elevated temperature, wherein the composite catalyst contains the solid acid catalyst in an amount of 36 to 65% by weight and the balance being the solid base catalyst, and wherein the temperature is higher than a temperature at which pH values of the (H.sub.2O/O.sub.2 redox) potential and (H.sub.2O/H.sub.2 redox) potential are equal to each other, the redox potentials being given by a water potential--pH value diagram.