Pour the milk into a pan, and heat over medium heat until small bubbles form around the edge of the pan and milk is just below the boiling point. Do not let the milk boil. Remove from heat and cool. Skim off any skin that forms on the milk.
Pour the cooled milk into a yogurt maker, and stir in the yogurt, vanilla, and bananas. Cook according to manufacturer's directions, or at least 4 hours . If desired, strain yogurt through a fine sieve or coffee filter to remove the whey, and return to the yogurt maker. Refrigerate the yogurt overnight or another 8 hours to thicken further.