The production strain of the Bracteacoccus bullatus alga deposited in the Collection of Autotrophic Organisms of the Botanical Institute of the Academy of Sciences of the Czech Republic, Třeboň, Dukelská 135, under accession number CCALA 1120: Bracteacoccus bullatus, strain Cepák et Lukavský 2011/13, is utilizable as a source for the industrial production of oils having a high content of polyunsaturated fatty acids, in particular linoleic acid and α-linolenic acid, oleic acid and cis-vaccenic acid, for food supplements for humans, animals or as use for other applications. The invention also describes the method of producing oils having a high content of unsaturated fatty acids in a pilot plant.