Soybeans (i.e., Glycine max L. Merr.) possessing a novel genetic determinant for the reduced production of linolenic acid in the endogenously formed vegetable oil of the seeds are provided. Such genetic determinant is the homozygous recessive fan3fan3 gene pair that has been found to be capable of formation through mutagenesis. Once formed, such genetic determinant can be readily transferred to other soybean lines and cultivars where it is similarly expressed on a reliable basis under conventional field growing conditions. In a preferred embodiment a soybean plant possesses the combined presence of the homozygous recessive gene pairs (1) fan1fan1 or fan1(A5)fan1(A5), (2) fan2fan2, as well as (3) fan3fan3 for reduced linolenic acid formation in the seeds and has been found that an unusually low expression for linolenic acid production in the resulting vegetable oil of the seeds is provided that is less than 1.3 percent by weight and most preferably is no more than 1.1 percent by weight based on the total fatty acid content. A vegetable oil is made possible in this instance that is particularly well suited for frying applications in the absence of the need for hydrogenation.