The invention relates to a method of obtaining industrially-viable prebiotic oligosaccharides, using a novel extracellular enzyme (fructofuranosidase) of Xanthophyllomyces dendrorhous, which is characterised in that it also has transfructosilase activity. The invention also relates to a method of obtaining an enzymatic product with fructofuranosidase activity, as well as the substantially-pure enzyme with said activity. The enzymatic product and the enzyme offer the advantage of having a high performance spectrum, high heat stability and a high specific activity. Said prebiotic oligosaccharaides are used in food.