A method of deacidizing a gaseous effluent including acid compounds includes the following stages: a) contacting the gaseous effluent with a first fraction of an absorbent solution containing reactive compounds with at least two amine functions, so as to obtain a gaseous effluent depleted in acid compounds and a liquid effluent laden with acid compounds, b) contacting the liquid effluent obtained in stage a) with a second fraction of absorbent solution laden with molecules more acid than the acid compounds, so as to cause formation of a first liquid phase depleted in acid compounds and a second liquid phase enriched in acid compounds and laden with more acid molecules, c) separating the first phase from the second phase, and d) regenerating the second phase so as to release a gas stream rich in acid compounds and a liquid stream poor in acid compounds and laden with more acid molecules.