Abstract: The method and the system for capturing the carbon dioxide present in flue-gas implement a) a first cooler device (110, 120) for cooling flue-gas and comprising at least one heat exchanger (122) for eliminating a fraction of the water present in the flue-gas by condensation; b) a flue-gas dehydration device (130); c) a second cooler device (140) for cooling the flue-gas and comprising at least one heat exchanger (141, 142) for bringing the flue-gas to a temperature that causes anti-sublimation of the carbon dioxide present in the flue-gas; d) a heater device (141, 142) in a closed enclosure for heating the solidified carbon dioxide to cause it to melt; and e) a device (144) for drawing off or pumping liquid and/or gaseous carbon dioxide to a thermally insulated tank (150).