A method for removing acid compounds contained in a gaseous effluent, comprising: - carrying out an acid compound absorption stage by contacting the effluent with an absorbent solution so as to obtain a gaseous effluent depleted in acid compounds and an absorbent solution laden with acid compounds, the absorbent solution containing: a- water, b- at least one amine of formula (N,N,N',N'-tetramethylhexane-1,6-diamine) c- at least one activating compound selected from among N-ButylPiperazine and a compound meeting formula wherein: n=1 or 2, each group R1, R2, R3, R4, R5, R6, R7 and R is selected independently from among one of the elements of the group made up of: a hydrogen atom, an alkyl group with 1 to 2 carbon atoms, and group R has one of the following characteristics: - group R is not linked to any one of groups R1 to R7, - group R is linked by R3 or R7 to the aromatic ring of formula so as to form a heterocycle with 5 or 6 atoms, and - carrying out a regeneration stage wherein at least part of the solution laden with acid compounds is sent to a distillation column so as to release the acid compounds in form of a gaseous effluent and to obtain a regenerated absorbent solution. - carrying out an acid compound absorption stage by contacting the effluent with an absorbent solution so as to obtain a gaseous effluent depleted in acid compounds and an absorbent solution laden with acid compounds, the absorbent solution containing: a- water, b- at least one amine of formula (N,N,N',N'-tetramethylhexane-1,6-diamine) c- at least one activating compound selected from among N-ButylPiperazine and a compound meeting formula wherein: n=1 or 2, each group R1, R2, R3, R4, R5, R6, R7 and R is selected independently from among one of the elements of the group made up of: a hydrogen atom, an alkyl group with 1 to 2 carbon atoms, and group R has one of the following characteristics: - group R is not linked to any one of groups R1 to R7, - group R is linked by R3 or R7 to the aromatic ring of formula so as to form a heterocycle with 5 or 6 atoms, and - carrying out a regeneration stage wherein at least part of the solution laden with acid compounds is sent to a distillation column so as to release the acid compounds in form of a gaseous effluent and to obtain a regenerated absorbent solution. a- water, b- at least one amine of formula (N,N,N',N'-tetramethylhexane-1,6-diamine) c- at least one activating compound selected from among N-ButylPiperazine and a compound meeting formula n=1 or 2, each group R1, R2, R3, R4, R5, R6, R7 and R is selected independently from among one of the elements of the group made up of: a hydrogen atom, an alkyl group with 1 to 2 carbon atoms, and group R has one of the following characteristics: - group R is not linked to any one of groups R1 to R7, - group R is linked by R3 or R7 to the aromatic ring of formula so as to form a heterocycle with 5 or 6 atoms, and - carrying out a regeneration stage wherein at least part of the solution laden with acid compounds is sent to a distillation column so as to release the acid compounds in form of a gaseous effluent and to obtain a regenerated absorbent solution. - group R is not linked to any one of groups R1 to R7, - group R is linked by R3 or R7 to the aromatic ring of formula so as to form a heterocycle with 5 or 6 atoms, and - carrying out a regeneration stage wherein at least part of the solution laden with acid compounds is sent to a distillation column so as to release the acid compounds in form of a gaseous effluent and to obtain a regenerated absorbent solution.