Process for the preparation of a zeolite of AFX structural type comprising at least the following stages: i) the mixing, in an aqueous medium, of a zeolite of FAU structural type, having an SiO 2 /Al 2 O 3 molar ratio of between 2.00 (limit included) and 6.00 (limit excluded), of a nitrogenous organic compound R, R being chosen from 1,5-bis(methylpiperidinium)pentane dihydroxide, 1,6-bis(methylpiperidinium)hexane dihydroxide or 1,7-bis(methylpiperidinium)heptane dihydroxide, of at least one source of at least one alkali and/or alkaline earth metal M of valency n, n being an integer greater than or equal to 1, M being sodium and the source of at least one alkali and/or alkaline earth metal M is sodium hydroxide, in the presence or not, of an additional supply, within said mixture, of at least one source of at least one tetravalent element XO 2, and/or of at least one source of at least one trivalent element Y 2 O 3, the reaction mixture exhibiting the following molar composition: (SiO 2)/(Al 2 O 3) of between 2.00 (limit included) and 6.00 (limit excluded), preferably between 3.00 (limit included) and 6.00 (limit excluded), H 2 O/(SiO 2) of between 1 and 100, preferably between 5 and 60, R/(SiO 2) of between 0.01 and 0.6, preferably between 0.05 and 0.5, M 2/n O/(SiO 2) of between 0.005 and 0.7, preferably between 0.05 and 0.6, limits included, in which SiO 2 denotes the amount of SiO 2 contributed by the FAU zeolite and Al 2 O 3 denotes the amount of Al 2 O 3 contributed by the FAU zeolite, until a homogeneous precursor gel exhibiting a molar ratio of the total amount, expressed as oxides, of tetravalent elements to the total amount, expressed as oxides, of trivalent elements of between 2 and 80 is obtained; ii) the hydrothermal treatment of said precursor gel obtained on conclusion of stage i) at a temperature of between 120°C and 220°C, for a period of time of between 12 hours and 15 days. i) the mixing, in an aqueous medium, of a zeolite of FAU structural type, having an SiO 2 /Al 2 O 3 molar ratio of between 2.00 (limit included) and 6.00 (limit excluded), of a nitrogenous organic compound R, R being chosen from 1,5-bis(methylpiperidinium)pentane dihydroxide, 1,6-bis(methylpiperidinium)hexane dihydroxide or 1,7-bis(methylpiperidinium)heptane dihydroxide, of at least one source of at least one alkali and/or alkaline earth metal M of valency n, n being an integer greater than or equal to 1, M being sodium and the source of at least one alkali and/or alkaline earth metal M is sodium hydroxide, in the presence or not, of an additional supply, within said mixture, of at least one source of at least one tetravalent element XO 2, and/or of at least one source of at least one trivalent element Y 2 O 3, the reaction mixture exhibiting the following molar composition: (SiO 2)/(Al 2 O 3) of between 2.00 (limit included) and 6.00 (limit excluded), preferably between 3.00 (limit included) and 6.00 (limit excluded), H 2 O/(SiO 2) of between 1 and 100, preferably between 5 and 60, R/(SiO 2) of between 0.01 and 0.6, preferably between 0.05 and 0.5, M 2/n O/(SiO 2) of between 0.005 and 0.7, preferably between 0.05 and 0.6, limits included, in which SiO 2 denotes the amount of SiO 2 contributed by the FAU zeolite and Al 2 O 3 denotes the amount of Al 2 O 3 contributed by the FAU zeolite, until a homogeneous precursor gel exhibiting a molar ratio of the total amount, expressed as oxides, of tetravalent elements to the total amount, expressed as oxides, of trivalent elements of between 2 and 80 is obtained; (SiO 2)/(Al 2 O 3) of between 2.00 (limit included) and 6.00 (limit excluded), preferably between 3.00 (limit included) and 6.00 (limit excluded), H 2 O/(SiO 2) of between 1 and 100, preferably between 5 and 60, R/(SiO 2) of between 0.01 and 0.6, preferably between 0.05 and 0.5, M 2/n O/(SiO 2) of between 0.005 and 0.7, preferably between 0.05 and 0.6, limits included, in which SiO 2 denotes the amount of SiO 2 contributed by the FAU zeolite and Al 2 O 3 denotes the amount of Al 2 O 3 contributed by the FAU zeolite, until a homogeneous precursor gel exhibiting a molar ratio of the total amount, expressed as oxides, of tetravalent elements to the total amount, expressed as oxides, of trivalent elements of between 2 and 80 is obtained; ii) the hydrothermal treatment of said precursor gel obtained on conclusion of stage i) at a temperature of between 120°C and 220°C, for a period of time of between 12 hours and 15 days.