Abstract: A process for producing a triglyceride mix free from components hampering further processing from a vegetable oil as a starting material, which is cooled and then separated into a predominantly solid and a predominantly liquid phase. The vegetable oil used as starting material is one in which a predetermined reactive fatty acid predominates in the fatty acid pattern with a content of at least about 80%. The cooling temperature of the cooling step is so adjusted that the particularly hard to solidify or readily soluble triglycerides in the starting material remain at least substantially liquid or in solution. In one embodiment, the solid phase obtained after the first separation step is then dissolved and cooled in a second cooling step to a temperature different from an initial temperature step at which the easier to solidify or less soluble triglycerides bearing less reactive groups separate out.