A METHOD FOR MANUFACTURING A REFINED FAT OR OIL, INCLUDING: CARRYING OUT A FIRST STEAM TREATMENT OF BRINGING A FAT OR OIL INTO CONTACT WITH WATER VAPOR AND SUBSEQUENTLY CARRYING OUT A SECOND STEAM TREATMENT OF BRINGING THE FAT OR OIL HAVING A TEMPERATURE LOWER BY 10°C OR MORE THAN A TEMPERATURE OF THE FAT OR OIL IN THE FIRST STEAM TREATMENT INTO CONTACT WITH WATER VAPOR IN THE PRESENCE OF AN ORGANIC ACID.