The classical extreme-value theory does not give a good account of the distribution of maximum rainfall intensities in Belgium. Reasons are given for the use, in this case, of a probability function defined by a double exponential whose argument is a function represented by a curve with two asymptotes. The application of such a probability function, when the curve is a branch of a hyperbola, to the maximum rainfall, in 1 min.; at Uccle, leads to a good fit.