Process for preparing a catalyst containing an active cobalt phase, deposited on a support comprising alumina, silica or silica-alumina, said support containing a mixed oxide phase containing cobalt and/or nickel, said catalyst being prepared by a process comprising at least: a) a step of bringing a support comprising alumina, silica or silica-alumina into contact with at least one solution containing at least one precursor of cobalt and/or of nickel, then drying at a temperature below 200°C and calcining at a temperature between 700°C and 1200°C, so as to obtain a mixed oxide phase containing cobalt and/or nickel in the support, then carrying out b) a step of bringing said support containing said mixed oxide phase into contact with at least one solution containing at least one precursor of cobalt, c) a step of bringing said support containing said mixed oxide phase into contact with at least one organic compound of the family of dilactones, selected from the group of cyclic dilactones having 4 ring members, consisting of 1,2-dioxetanedione, or from the group of cyclic dilactones having 5 ring members, consisting of 1,3-dioxolane-4,5-dione, 1,5-dioxolane-2,4-dione and 2,2-dibutyl-1,5-dioxolane-2,4-dione, or from the group of cyclic dilactones having 6 ring members, consisting of 1,3-dioxane-4,6-dione, 2,2-dimethyl-1,3-dioxane-4,6-dione, 2,2,5-trimethyl-1,3-dioxane-4,6-dione, 1,4-dioxane-2,5-dione, 3,6-dimethyl-1,4-dioxane-2,5-dione, 3,6-diisopropyl-1,4-dioxane-2,5-dione and 3,3-ditolyl-6,6-diphenyl-1,4-dioxane-2,5-dione, or from the group of cyclic dilactones having 7 ring members, consisting of 1,2-dioxepane-3,7-dione, 1,4-dioxepane-5,7-dione, 1,3-dioxepane-4,7-dione and 5-hydroxy-2,2-dimethyl-1,3-dioxepane-4,7-dione, it being possible for steps b) and c) to be performed separately, in any order, or simultaneously, d) then carrying out a step of drying at a temperature below 200°C. a) a step of bringing a support comprising alumina, silica or silica-alumina into contact with at least one solution containing at least one precursor of cobalt and/or of nickel, then drying at a temperature below 200°C and calcining at a temperature between 700°C and 1200°C, so as to obtain a mixed oxide phase containing cobalt and/or nickel in the support, then carrying out b) a step of bringing said support containing said mixed oxide phase into contact with at least one solution containing at least one precursor of cobalt, c) a step of bringing said support containing said mixed oxide phase into contact with at least one organic compound of the family of dilactones, selected from the group of cyclic dilactones having 4 ring members, consisting of 1,2-dioxetanedione, or from the group of cyclic dilactones having 5 ring members, consisting of 1,3-dioxolane-4,5-dione, 1,5-dioxolane-2,4-dione and 2,2-dibutyl-1,5-dioxolane-2,4-dione, or from the group of cyclic dilactones having 6 ring members, consisting of 1,3-dioxane-4,6-dione, 2,2-dimethyl-1,3-dioxane-4,6-dione, 2,2,5-trimethyl-1,3-dioxane-4,6-dione, 1,4-dioxane-2,5-dione, 3,6-dimethyl-1,4-dioxane-2,5-dione, 3,6-diisopropyl-1,4-dioxane-2,5-dione and 3,3-ditolyl-6,6-diphenyl-1,4-dioxane-2,5-dione, or from the group of cyclic dilactones having 7 ring members, consisting of 1,2-dioxepane-3,7-dione, 1,4-dioxepane-5,7-dione, 1,3-dioxepane-4,7-dione and 5-hydroxy-2,2-dimethyl-1,3-dioxepane-4,7-dione, it being possible for steps b) and c) to be performed separately, in any order, or simultaneously, d) then carrying out a step of drying at a temperature below 200°C.