Pre-heat oven to 350°F.
Lightly grease a 9 × 5-inch loaf pan.
Lightly flour the bottom and sides of the loaf pan.
In a large bowl, combine flour, baking soda and salt.
In a separate bowl, mix together applesauce and honey.
To the applesauce and honey mixture, add eggs and mashed bananas; stir until well blended.
Stir banana mixture into flour mixture; stir just to moisten.
Pour batter into prepared loaf pan.
Bake for 60 to 65 minutes, until a toothpick inserted into center of the loaf comes out clean.
Let bread cool in pan for 10 minutes, then turn out onto a wire rack.
