Method for producing argon by cryogenic distillation wherein an argon-enriched gas produced by air separation in a system of columns is sent to an argon separation column, an argon-rich flow is drawn off at the top of the column and an oxygen-rich liquid is drawn off at the tank of the column and sent back to the system of columns wherein: i) during a first step, if, preferably only if, the load of the column is below a first threshold, liquid is drawn off from the column at a first intermediate level of the column and stored in a first storage facility (S1, S2, S3, S4, S5, S6), with no liquid being sent from the first storage facility to the column and liquid is drawn off from the column at a third intermediate level of the column and stored in a second storage facility (S1, S2, S3, S4, S5), with no liquid being sent from the second storage facility to the column, ii) during a second step, if, preferably only if, the load of the column is above a second threshold, greater than the first threshold, no liquid is sent from the column to the first storage facility, liquid is sent from the first storage facility to the column at a second intermediate level of the column, the second level being located below the first level, no liquid is sent from the column to the second storage facility, liquid is sent from the second storage facility to the column at a fourth intermediate level of the column, the fourth level being located below the third level and the third level not being located above the second level characterised in that the second level is separated from the first level by at least one layer of elements (2, 3, 4, 5, 6, 7) allowing for the exchange of mass and heat and the fourth level is separated from the third level by at least one layer of elements (2, 3, 4, 5, 6) allowing for the exchange of mass and heat. i) during a first step, if, preferably only if, the load of the column is below a first threshold, liquid is drawn off from the column at a first intermediate level of the column and stored in a first storage facility (S1, S2, S3, S4, S5, S6), with no liquid being sent from the first storage facility to the column and liquid is drawn off from the column at a third intermediate level of the column and stored in a second storage facility (S1, S2, S3, S4, S5), with no liquid being sent from the second storage facility to the column, ii) during a second step, if, preferably only if, the load of the column is above a second threshold, greater than the first threshold, no liquid is sent from the column to the first storage facility, liquid is sent from the first storage facility to the column at a second intermediate level of the column, the second level being located below the first level, no liquid is sent from the column to the second storage facility, liquid is sent from the second storage facility to the column at a fourth intermediate level of the column, the fourth level being located below the third level and the third level not being located above the second level characterised in that the second level is separated from the first level by at least one layer of elements (2, 3, 4, 5, 6, 7) allowing for the exchange of mass and heat and the fourth level is separated from the third level by at least one layer of elements (2, 3, 4, 5, 6) allowing for the exchange of mass and heat.