The present invention refers to the synthesis of 3-{[(2R)-1-methylpyrrolidin-2-yl]methyl}-5-[2-(phenylsulfonyl)ethyl]-1H-indole, a drug known by the name Eletriptan, or of its salts. In particular, the present invention regards a process for the synthesis of Eletriptan or of its salt, comprising the following steps: a) Salifying the intermediate of Formula (6), using a dicarboxylic acid to obtain a derived salt; b) Optionally, purifying said raw salt obtained according to step a) by solvent crystallization to obtain a purified salt of the intermediate of Formula (6); c) Converting said salt of the intermediate of formula (6) according to step a) or said purified salt according to step b) into an intermediate of formula (10); d) Converting the intermediate of Formula (10) into Eletriptan or its salt.