NOVELTY - Synthesizing sitagliptin comprises hydrogenating (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid compound (I) to obtain (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid (VII), protecting (VII) to obtain (R)-3-tert-butoxycarbonylamino-4-(2,4,5-trifluoro-phenyl)-butyric acid (VIII), converting (VIII) into ((R)-3-oxo-1-(2,4,5-trifluoro-benzyl)-3-(3-trifluoromethyl-5,6-dihydro-8H-(1,2,4)triazolo(4,3-a)pyrazin-7-yl)-propyl)-carbamic acid tert-butyl ester (IX), and deprotecting (IX).    USE - The method is useful for synthesizing sitagliptin (claimed).    ADVANTAGE - The method simply provides sitagliptin with high yield and purity in a cost-effective and eco-friendly manner and is especially beneficial for industrial production.    DETAILED DESCRIPTION - Synthesizing sitagliptin comprises hydrogenating (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid compound of formula (I) to obtain (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid (VII), protecting (VII) to obtain (R)-3-tert-butoxycarbonylamino-4-(2,4,5-trifluoro-phenyl)-butyric acid (VIII), converting (VIII) into ((R)-3-oxo-1-(2,4,5-trifluoro-benzyl)-3-(3-trifluoromethyl-5,6-dihydro-8H-(1,2,4)triazolo(4,3-a)pyrazin-7-yl)-propyl)-carbamic acid tert-butyl ester (IX), and deprotecting (IX) to obtain (R)-3-amino-1-(3-trifluoromethyl-5,6-dihydro-8H-(1,2,4)triazolo(4,3-a)pyrazin-7-yl)-4-(2,4,5-trifluoro-phenyl)-butan-1-one (X).    R1 = benzyl (optionally substituted);    R2, R3 = H or benzyl, where the phenyl group in benzyl is optionally substituted with 1-3 substituents of halo, nitryl, 1-12C alkyl and 1-12C alkoxy.    An INDEPENDENT CLAIM is included for synthesizing (I) comprising reacting 5-(1-hydroxy-2-(2,4,5-trifluoro-phenyl)-ethyl)-2,2-dimethyl-(1,3)dioxane-4,6-dione (II) with benzyl alcohol or substituted benzyl alcohol as a raw material to obtain 3-oxo-4-(2,4,5-trifluoro-phenyl)-butyric acid compound of formula (III), processing obtained (III) using ammonia, ammonium formate, ammonium acetate to obtain (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid compound of formula (IV), reducing (IV) using reducing agent to obtain (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid compound of formula (V), resolving (V) in a presence of solvent using chiral resolution reagent to obtain (R)-3-amino-4-(2,4,5-trifluoro-phenyl)-butyric acid compound of formula (VI), and processing obtained (VI) using alkali.