A process for obtaining the pharmaceutical active ingredient, levetiracetam, by means of deaminomethylation of a sufficiently pure enantiomer intermediate (S)-(II), or by means of deaminomethylation of an addition salt thereof with an acid, wherein R1 and R2 are either the same or different (C1-C6)-alkyl radicals, or else R1 and R2 together with the nitrogen atom to which they are bonded form a radical selected from the group consisting of 1-pyrrolidinyl, 1-piperidinyl, 1-morpholinyl, 1-piperazinyl and 1-[4-(C1-C4)-alkylpiperazinyl]. The invention also comprises preparing the sufficiently pure enantiomer intermediate (S)-(II) by treating the corresponding chemically new racemic intermediate (II) with an amine resolving agent, followed by selective crystallisation of a diastereoisomeric salt thereof. It is useful for obtaining levetiracetam on an industrial scale and involves neither hydrogenation nor chromatography.