THE PRESENT INVENTION RELATES TO A PROCESS FOR THE PRODUCTION OF A FAT COMPOSITION FOR CONFECTIONERY OR BAKING APPLICATIONS. ACCORDING TO THIS PROCESS, A STARTING FAT COMPOSITION CONTAINING PALM OIL OR A PALM OIL FRACTION AND HAVING THE FOLLOWING COMPOSITION: (1) A GLYCERIDE COMPOSTION WITH - A S2U CONTENT BETWEEN 47 AND 75 wt. %,- A SU2 + U3 CONTENT <; 40 wt. %,- A S3 CONTENT BETWEEN 1 AND15 wt. %,- A DIGLYCERIDE CONTENT OF 3 TO 12 wt. %, THE GLYCERIDE CONTENTS BEING EXPRESSED AS wt. % WITH RESPECT TO THE TOTAL AMOUNT OF DI- AND TRIGLYCERIDES IN WHICH S MEANS A SATURATED FATTY ACID WITH A HYDROCARBON CHAIN LENGTH OF 14-24 CARBON ATOMS AND U MEANS UNSATURATED FATTY ACID WITH A HYDROCARBON CHAIN LENGTH OF 14-24 CARBON ATOMS AND (2) A TOTAL CONTENT OF UNSATURATED FATTY ACIDS OF LESS THAN 55 wt. % , PREFERABLY LESS THAN 50 wt. %, MORE PREFERABLY LESS THAN 48 wt. %, IS SUBJECTED TO A CATALYTIC HYDROGENATION SO AS TO OBTAIN A FIRST FAT WITH A TRANS FATTY ACID CONTENT <;wt. %, PREFERABLY <; 10 wt. % , MOST PREFERABLY <; 5 wt. % AND AN INCREASE OF C18-0 OF LESS THAN 1 wt.% , PREFERABLY LESS THAN 0.7 wt. % , MORE PREFERABLY LESS THAN 0.4 wt. % THIS FIRST FAT IS INCORPORATED IN THE FAT COMPOSITION.