A method for the direct synthesis of a crystalline material with the AEI zeolithic structure containing iron-species and being essentially free of alkali ions, comprising the following steps: (i) preparation of a mixture consisting of water, a high-silica zeolite as a main source of silica and alumina, wherein the high-silica zeolite has the FAU framework structure and a Si/AI atomic ratio above 5; an alkyl-substituted cyclic ammonium cation as organic structure directing agent (OSDA), wherein the OSDA is selected from N,N-dimethyl-3,5-dimethylpiperidinium (DMDMP), N,N-diethyl-2,6-dimethylpiperidinium, N,N-dimethyl-2,6-dime-thylpiperidinium, N-ethyl-N-methyl-2,6-dimethylpiperidinium, and combinations thereof; a source of iron, wherein the source of iron is an iron salt, and wherein the iron salt is selected from one or more salts of halides, acetates, nitrates, sulfates, and mixtures thereof, and a source of an alkali metal ion [Alk], to obtain a final synthesis mixture having the following molar composition: SiO 2: a Al 2 O 3: b Fe: c OSDA: d Alk: e H 2 O wherein a is in the range from 0.001 to 0.2; wherein b is in the range from 0.001 to 0.2; wherein c is in the range from 0.01 to 2; wherein d is in the range from 0.001 to 2; wherein e is in the range from 1 to 200; (ii) crystallization of the mixture achieved in (i); (iii) recovery of the crystalline material achieved in (ii); (iv) calcination of the crystalline material from step (iii); and (v) removal of the alkali metal cation, present in the calcined crystalline material after step (iv) by ion exchange with ammonium ions or hydrogen ions to obtain a final molar composition: SiO 2: o Al 2 O 3: p Fe: q Alk wherein o is in the range from 0.001 to 0.2, p is in the range from 0.001 to 0.2 and q is below 0.02. (i) preparation of a mixture consisting of water, a high-silica zeolite as a main source of silica and alumina, wherein the high-silica zeolite has the FAU framework structure and a Si/AI atomic ratio above 5; an alkyl-substituted cyclic ammonium cation as organic structure directing agent (OSDA), wherein the OSDA is selected from N,N-dimethyl-3,5-dimethylpiperidinium (DMDMP), N,N-diethyl-2,6-dimethylpiperidinium, N,N-dimethyl-2,6-dime-thylpiperidinium, N-ethyl-N-methyl-2,6-dimethylpiperidinium, and combinations thereof; a source of iron, wherein the source of iron is an iron salt, and wherein the iron salt is selected from one or more salts of halides, acetates, nitrates, sulfates, and mixtures thereof, and a source of an alkali metal ion [Alk], to obtain a final synthesis mixture having the following molar composition: SiO 2: a Al 2 O 3: b Fe: c OSDA: d Alk: e H 2 O wherein a is in the range from 0.001 to 0.2; wherein b is in the range from 0.001 to 0.2; wherein c is in the range from 0.01 to 2; wherein d is in the range from 0.001 to 2; wherein e is in the range from 1 to 200; wherein a is in the range from 0.001 to 0.2; wherein b is in the range from 0.001 to 0.2; wherein c is in the range from 0.01 to 2; wherein d is in the range from 0.001 to 2; wherein e is in the range from 1 to 200; (ii) crystallization of the mixture achieved in (i); (iii) recovery of the crystalline material achieved in (ii); (iv) calcination of the crystalline material from step (iii); and (v) removal of the alkali metal cation, present in the calcined crystalline material after step (iv) by ion exchange with ammonium ions or hydrogen ions to obtain a final molar composition: SiO 2: o Al 2 O 3: p Fe: q Alk