The method enables the antihydrate compounds contained in a condensed-hydrocarbon liquid feedstock arriving through pipe 1 to be extracted. The liquid feedstock is brought into contact, in zone ZA, with a non-aqueous ionic liquid having the general formula Q+ A31 , where Q+ designates an ammonium, phosphonium, and/or sulfonium cation, and A31 designates an anion able to form a liquid salt. The antihydrate compounds in the liquid hydrocarbon feedstock evacuated through pipe 2 are eliminated. The ionic liquid charged with antihydrate compounds is evacuated through pipe 3, then introduced into evaporator DE to be heated in order to evaporate the antihydrate compounds. The regenerated ionic liquid is recycled through pipes 8 and 9 to zone ZA. The antihydrates are evacuated through pipe 7a.