A method of synthesising an amino acid from an unsaturated fatty compound I that includes at least the following steps: cross-metathesis with a short unsaturated compound II, one of compounds I or II comprising a nitrile function and the other of these compounds II or I an ester function, so as to obtain and recover at least one monounsaturated nitrile ester NEU; hydrolysis of the NEU in unsaturated acid nitrile NAU; hydrogenation of the NAU to saturated amino acid AA; and then purification of the AA, if applicable, in particular by crystallisation. Also, a polymer obtained by polymerisation using the amino acid synthesised according to the method.