The invention relates to a process of producing polyunsaturated fatty acids through the incorporation of olefinic or acetylenic fatty acids with a chain length of 13-18 carbon atoms as substrates with a haploid or diploid wild strain of Saccharomyces cerevisiae yeast W 303a or .DELTA.Elo1, which can be used to generate a novel linkage with configuration Z in position 9 of said substrates. The novel desaturation is only produced if the original unsaturation in the administered products has configuration E or is an acetylene. Moreover, if the original linkage has configuration Z, the substrate is recovered unaltered.