A process for obtaining fatty alcohols from fatty acid methyl ester (FAME), characterized in that the following steps are comprised: (a) supplying a feed stream containing fatty acid methyl ester to a hydrogenation stage, conversion of the feed stream in the presence of hydrogen under hydrogenation conditions on a bed of solid, granular hydrogenation catalyst, discharging a first material stream containing fatty alcohol, methanol and non-converted FAME, (b) supplying the first material stream to a distillation stage, separating the methanol as top product of the distillation, and discharging the bottom product of the distillation as second material stream comprising fatty alcohol and FAME, (c) supplying the second material stream to a transesterification reactor filled with a bed of solid, granular catalyst, transesterification of the second material stream under transesterification conditions to a third material stream comprising fatty alcohol and wax ester in counterflow with an inert gas stream as stripping gas stream, wherein the methanol produced during the transesterification is separated with the stripping gas as top product and the third material stream comprising fatty alcohol and wax ester is discharged, (d) supplying the third material stream to a separation stage operating by a thermal separation process, separating a fourth material stream enriched in wax ester, discharging a fifth material stream depleted of wax ester and enriched in fatty alcohol as fatty alcohol product stream, (e) recirculating the fourth material stream enriched in wax ester to the hydrogenation stage (a), characterized in that in process step (c) a transesterification catalyst on the basis of magnesium oxide or hydrotalcite is used. (a) supplying a feed stream containing fatty acid methyl ester to a hydrogenation stage, conversion of the feed stream in the presence of hydrogen under hydrogenation conditions on a bed of solid, granular hydrogenation catalyst, discharging a first material stream containing fatty alcohol, methanol and non-converted FAME, (b) supplying the first material stream to a distillation stage, separating the methanol as top product of the distillation, and discharging the bottom product of the distillation as second material stream comprising fatty alcohol and FAME, (c) supplying the second material stream to a transesterification reactor filled with a bed of solid, granular catalyst, transesterification of the second material stream under transesterification conditions to a third material stream comprising fatty alcohol and wax ester in counterflow with an inert gas stream as stripping gas stream, wherein the methanol produced during the transesterification is separated with the stripping gas as top product and the third material stream comprising fatty alcohol and wax ester is discharged, (d) supplying the third material stream to a separation stage operating by a thermal separation process, separating a fourth material stream enriched in wax ester, discharging a fifth material stream depleted of wax ester and enriched in fatty alcohol as fatty alcohol product stream, (e) recirculating the fourth material stream enriched in wax ester to the hydrogenation stage (a),