Soybeans (i.e., Glycine max L. Merr.) possessing a novel genetic determinant for the enhanced production of palmitic acid in the endogenously formed vegetable oil of the seeds are provided. Such genetic determinant is the homogeneous recessive fap5fap5 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 when a soybean plant possesses the combined presence of the homogeneous recessive genes (1) fap2-bfap2-b, (2) fap4fap4, as well as (3) fap5fap5 for enhanced palmitic acid formation in the seeds, it has been found that an unusually high expression for palmitic acid production in the resulting vegetable oil of the seeds is provided that is in excess of 30 up to approximately 37 percent by weight based upon the total fatty acid content. A resulting vegetable oil is made possible in this instance that is particularly well suited for margarine preparation in absence of the need for hydrogenation.