In a purification method, a carbon dioxide-rich gas is cooled in a first brazed aluminum plate-fin heat exchanger, the cooled gas or at least one fluid derived from the cooled gas is sent to a purification step comprising a distillation step, the purification step produces a carbon dioxide-rich liquid which is cooled, then expanded, then sent to a second heat exchanger where it is heated by means of a fluid of the method, the exchanger carrying out an indirect heat exchange only between the carbon dioxide-rich liquid and the fluid of the method, the carbon dioxide-rich liquid at least partially vaporizes in the second exchanger and the vaporized gas formed heats up again in the first exchanger to form a carbon dioxide-rich gas.