Method for revamping a refining section of a methanol distillation plant, said refining section receiving a stream of crude methanol and comprising a medium pressure refining column arranged to operate at a first distillation pressure and a low pressure refining column arranged to operate at a second distillation pressure, wherein p1 is higher than p2 and wherein: said MP refining column and said LP refining column each comprises at least one bottom boiler (301, 401) providing distillation heat to the MP column and the LP column, respectively, said MP refining column comprises a top outlet line for a gaseous stream of distilled methanol and a bottom outlet line for a solution containing methanol, said top outlet line being directed to at least one bottom boiler of the LP refining column, wherein said gaseous stream of distilled methanol acts as a heat source, and said bottom outlet line being directed to the LP refining column, wherein said solution containing methanol is further refined, the method being characterized by: installation of a high pressure refining column arranged to operate at a third distillation pressure, wherein p3 is higher than p1; installation of a line feeding a gaseous stream of distilled methanol withdrawn from the top of said HP column to at least one bottom boiler of the MP column, wherein said gaseous stream of distilled methanol acts as a heat source, and installation of a bottom outlet line for exporting a liquid stream consisting essentially of water from the newly installed HP column. said MP refining column and said LP refining column each comprises at least one bottom boiler (301, 401) providing distillation heat to the MP column and the LP column, respectively, said MP refining column comprises a top outlet line for a gaseous stream of distilled methanol and a bottom outlet line for a solution containing methanol, said top outlet line being directed to at least one bottom boiler of the LP refining column, wherein said gaseous stream of distilled methanol acts as a heat source, and said bottom outlet line being directed to the LP refining column, wherein said solution containing methanol is further refined, the method being characterized by: installation of a high pressure refining column arranged to operate at a third distillation pressure, wherein p3 is higher than p1; installation of a line feeding a gaseous stream of distilled methanol withdrawn from the top of said HP column to at least one bottom boiler of the MP column, wherein said gaseous stream of distilled methanol acts as a heat source, and installation of a bottom outlet line for exporting a liquid stream consisting essentially of water from the newly installed HP column. installation of a high pressure refining column arranged to operate at a third distillation pressure, wherein p3 is higher than p1; installation of a line feeding a gaseous stream of distilled methanol withdrawn from the top of said HP column to at least one bottom boiler of the MP column, wherein said gaseous stream of distilled methanol acts as a heat source, and installation of a bottom outlet line for exporting a liquid stream consisting essentially of water from the newly installed HP column.