A method for manufacturing linear alpha olefins, wherein - ethylene in a feed mixture is subjected to catalytic oligomerization to obtain a product mixture containing alpha olefins with different chain lengths and secondary compounds, - a primary fraction is formed in a primary fractionation using at least a portion of the product mixture, and a secondary fraction is formed in a secondary fractionation using at least a portion of the primary fraction, - the primary fractionation and secondary fractionation are carried out such that the primary fraction and the secondary fraction predominantly contain one of the alpha olefins and are low in or free from other alpha olefins, the primary fraction contains one or more of the secondary compounds, and the secondary fraction, compared to the primary fraction, is depleted of or free from the one or more secondary compounds, and - in an intermediate step between the primary fractionation and the secondary fractionation, to which step at least a portion of the primary fraction is subjected, the one or more secondary compounds are at least partially converted to one or more subsequent compounds, and the one or more subsequent compounds are at least partially separated off in the secondary fractionation, - wherein the alpha olefin which is predominantly contained in the primary fraction and the secondary fraction is 1-hexene, the secondary compound or one of the secondary compounds is 2-ethyl-1-butene, and the subsequent compound or one of the subsequent compounds is 3-methyl-2-pentene, or wherein the alpha olefin which is predominantly contained in the primary fraction and the secondary fraction is 1-octene, the secondary compound or one of the secondary compounds is 2-ethyl-1-hexene, and the subsequent compound or one of the subsequent compounds is 3-methyl-1-heptene, characterized in that - the intermediate step is carried out using chi and gamma dialuminum trioxide as catalyst, so that no more than 0.8% of the alpha olefin predominantly contained in the primary fraction or the portion thereof subjected to the intermediate step is converted. - ethylene in a feed mixture is subjected to catalytic oligomerization to obtain a product mixture containing alpha olefins with different chain lengths and secondary compounds, - a primary fraction is formed in a primary fractionation using at least a portion of the product mixture, and a secondary fraction is formed in a secondary fractionation using at least a portion of the primary fraction, - the primary fractionation and secondary fractionation are carried out such that the primary fraction and the secondary fraction predominantly contain one of the alpha olefins and are low in or free from other alpha olefins, the primary fraction contains one or more of the secondary compounds, and the secondary fraction, compared to the primary fraction, is depleted of or free from the one or more secondary compounds, and - in an intermediate step between the primary fractionation and the secondary fractionation, to which step at least a portion of the primary fraction is subjected, the one or more secondary compounds are at least partially converted to one or more subsequent compounds, and the one or more subsequent compounds are at least partially separated off in the secondary fractionation, - wherein the alpha olefin which is predominantly contained in the primary fraction and the secondary fraction is 1-hexene, the secondary compound or one of the secondary compounds is 2-ethyl-1-butene, and the subsequent compound or one of the subsequent compounds is 3-methyl-2-pentene, or wherein the alpha olefin which is predominantly contained in the primary fraction and the secondary fraction is 1-octene, the secondary compound or one of the secondary compounds is 2-ethyl-1-hexene, and the subsequent compound or one of the subsequent compounds is 3-methyl-1-heptene, - the intermediate step is carried out using chi and gamma dialuminum trioxide as catalyst, so that no more than 0.8% of the alpha olefin predominantly contained in the primary fraction or the portion thereof subjected to the intermediate step is converted.