Preheat the oven to 350°F and lightly grease a 9×5 inch loaf pan.
Combine the flour, baking soda and salt in a large mixing bowl.
In another bowl, cream together the butter and brown sugar. Stir in the eggs and mashed bananas until well blended.
Stir the banana mixture into the flour mixture just until moisten. Pour the batter into the prepared loaf pan.
Bake in the oven for 60-65 minutes or until a toothpick inserted in the middle comes out clean. Let the bread cool in the pan for 10 minutes, then turn out onto a wire rack.