A method for purification of a first polyunsaturated fatty acid from an initial mixture is provided. The initial mixture comprises at least one second fatty acid in addition to the first polyunsaturated fatty acid. The method may comprise separating the first polyunsaturated fatty acid and the second fatty acid in a liquid phase in at least one step of a chromatographic separation process, so as to recover, on the one hand, a stream enriched in the first polyunsaturated fatty acid, and on the other hand, a stream enriched in the second fatty acid. The method may further comprise a step of processing the stream enriched in the first polyunsaturated fatty acid to decrease the peroxide value and/or anisidine value of this stream. The disclosure also provides systems or devices suitably adapted for the implementation of such methods.