Abstract This paper studies the synthesis of triacylglycerols (TAGs) rich in palmitic acid (PA) at position 2, from palm oil stearin (POS), a vegetable oil highly rich in this acid (60%). The developed process consists of two steps: (1) obtaining PA enriched free fatty acids (FFAs), and (2) enrichment of POS in PA by acidolysis of this oil with PA enriched FFAs, catalyzed by lipase Novozym 435. In step (1) two PA enriched FFA mixtures were obtained: one by saponification of POS, and a PA concentrate (75.1% PA) obtained by crystallization at low temperature in solvents. The latter was obtained carrying out two crystallizations in acetone at −24 and −20 °C, from which PA was recovered in the solid phases with a total yield of 84%. These PA enriched FFA mixtures were used in step (2) of acidolysis of POS, along with commercial PA (98% PA). In this acidolysis step four factors were studied: temperature, hexane/reaction mixture ratio, FFA/POS molar ratio and the intensity of treatment (IOT = lipase amount × reaction time/POS amount). The best results (TAGs with 79% PA and 75% PA at position 2) were obtained with commercial PA, at 37 °C, 10 mL hexane/g reaction mixture, a FFA/POS molar ratio 3:1 (1:1, w/w) and an IOT = 9.6 g lipase × h/g POS (for example 48 h, 10 g lipase and 50 g POS). PA enriched TAGs were purified neutralizing the FFAs by KOH hydroethanolic solutions and extracting the TAGs with hexane. In this way 99% pure acylglycerols (TAG + DAG) were obtained; the recovery yield of this purification step was 95%. The experiments carried out with POS demonstrated that it is possible to use only this oil (60% PA, 23% PA at position 2) as a source of PA to obtain a TAG with 70.7% PA and 70.5% PA at position 2. This process consists of four steps: (1) saponification of POS, (2) crystallization of FFAs to obtain PA enriched FFAs (75.1% PA), (3) acidolysis of POS with these FFAs, catalyzed with Novozym 435, to produce PA enriched TAGs at position 2 (70.5% PA) and (4) purification of TAGs to obtain approximately 95% purity and yield. These PA enriched TAGs could be used to obtain structured TAGs rich in PA at position 2 and in oleic acid at positions 1 and 3 (OPO), which is the principal TAG of human milk fat.