Method for producing new fatty acids (I) in oil-producing yeasts (A) comprises (a) forming (A) by introducing into a parent yeast genes that encode the enzymes delta 5-, delta 6, delta 12- or delta 15-desaturases and elongase and (b) culturing the transformants in a medium with a high content of carbon sources. Independent claims are also included for the following: (1) residues obtained by pressing (A); and (2) (I) produced by the new method.