A method with which uranium from a natural uranium concentrate may be purified, including a) extracting the uranium present as uranyl nitrate in an aqueous phase A1 resulting from the dissolution of the natural uranium concentrate in nitric acid, by means of an organic phase which contains an extractant in an organic diluent; b) washing the organic phase obtained at the end of step a), with an aqueous phase A2; and c) stripping the uranyl nitrate of the organic phase obtained at the end of step b), by circulating this organic phase in an apparatus, as a counter current against an aqueous phase A3. The extractant is an N,N-dialkylamide and the ratio between the flow rate at which the organic phase obtained at the end of step b) and the aqueous phase A3 circulate in the apparatus where step c) occurs, is greater than 1.