Abstract: A self-refrigerated method of cryogenic fractionation and purification of gas and a heat exchanger for performing the method, wherein the gaseous fluid is treated in an exchanger forming a unitary assembly: it is partially condensed by cooling in a fifth and first circuits and the non-condensed gaseous fraction is re-heated in a second circuit, the required cold being supplied by the condensates which after having been sub-cooled in a third circuit and expanded in a valve are evaporating in a fourth circuit, the method permitting the purification of a gaseous fluid with several condensable components through cooling possibly in an exchanger with multiple channels for each circuit.