Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x5 inch loaf pan and set aside.

In a large bowl, combine flour, baking soda, baking powder, salt, and set aside. In a separate bowl, cream together butter and sugar. Stir in eggs, milk, vanilla, and mashed bananas until well blended. Stir banana mixture and walnuts into flour mixture; stir just to moisten. Pour batter into prepared loaf pan.

Bake in preheated oven for 50 to 55 minutes, until a toothpick inserted into center of the loaf comes out clean. Let bread cool in pan for at least 15 minutes, then turn out onto a wire rack and cool another 30 minutes. Slice and serve warm!