There's really no such thing as non-allergenic cats. However, you can get pretty close with "hypoallergenic cats." These felines are prone to shed less, or have less dander, which both are major causes of cat allergies.
Looking at this fuzzy breed, sometimes referred to as the "longhaired Siamese," you might not guess that it's among the least allergenic cats. That perhaps is due to a common misconception that cat hair itself triggers allergies, which is not exactly the case. The proteins that cause allergic reactions are present in a cat's saliva and skin oils, which are carried through the home by shed fur. But Balinese cats produce much less of the Fel D1 protein that causes allergies in the first place, so their fur carries less of the allergen around. (Catster)