The self-diffusion coefficient of water in a perfluorinated ionic membrane has been measured for different water contents corresponding to water vapor pressures less than the saturated one. The isotope method usually employed in the liquid state was extended to vapors, which led us to an observation of three different isotopic species by quantitative far IR spectroscopy. Two measurement methods are presented permitting a determination of the time lag and hence of the diffusion coefficient. The slow variation of the diffusion coefficient with the water concentration, as well as the good agreement of the numerical results given by different methods (permeation-sorption) are explained by the fact that no plasticization occurs. This result has been independently verified by other experiments.