In a method for vaporising a carbon dioxide-rich liquid flow in which a first carbon dioxide-rich liquid flow (5) is drawn from an enclosure (S1) containing carbon dioxide-rich liquid and carbon dioxide-rich gas, the gas being at pressure P1, the first liquid flow is sent to a heat exchanger (7) where it vaporises, all the liquid from the first flow vaporises in the heat exchanger at a pressure or a plurality of pressures greater than P1, the first vaporised flow is discharged from the heat exchanger, expanded in a first expansion valve (V2) and sent back to the heat exchanger, where it heats up again.