Preheat oven to 350 degrees f (175 degrees c). lightly grease a 9×5 inch loaf pan.
in a large bowl, combine flour, baking soda and salt. in a separate bowl, cream together butter and brown sugar. stir in eggs and mashed bananas until well blended. stir banana mixture into flour mixture; stir just to moisten. pour batter into prepared loaf pan.
bake in preheated oven 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.