Spray an 8x4 inch loaf pan with nonstick cooking spray.
In a large bowl, stir together flour, sugar, baking powder, baking soda and cinnamon. Add egg whites, bananas and applesauce; stir just until combined.
Pour batter into pan. Bake for 50 to 55 minutes, until a toothpick inserted into center of loaf comes out clean.
Transfer to a wire rack and let cool before slicing.