Abstract: The invention provides a method and a system for extracting a substance comprised in a gaseous mixture, the extraction being carried out in a cyclic manner in 2N chambers (AA, BB, CC, DD), each provided with a heat-exchanger (A, B, C, D), N being an integer greater than or equal to 3. Each chamber carries out a cycle comprising the following four steps in succession: a frosting step, a defrosting step, a step of recovering the liquid phase and the residual gas phase, and a temperature-reduction step of reducing the temperature of the heat-exchanger. Further, sequencing the passage from one step to another in each of the chambers is such that the number of chambers carrying out the frosting step and also the total number of chambers carrying out the defrosting, recovery, and temperature-reduction steps are both equal to N.