The present invention relates to a method of producing hydrogen of very high purity from a feed predominantly containing said hydrogen and a minor part of impurities mainly consisting of carbon dioxide, carbon monoxide, methane and heavier hydrocarbons. The purification method by hydrogen adsorption using a desorption stage at a lower pressure than the pressure of the feed, such as a PSA method for example, allows to produce the desorption stream and notably to recover the carbon dioxide under pressure and high-purity hydrogen, with a high yield. These performances are obtained by combining the successive stages of the method according to the invention with the use of a new family of adsorbent whose dynamic capacity at a high desorption pressure is greater than that of conventional adsorbents.