Preheat your oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan.
In a large bowl, combine flour, baking soda, and salt. Set aside.
In a separate 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; stir just to moisten. Pour batter into prepared loaf pan.
Bake in preheated oven for 60 minutes, until a toothpick inserted into the center of the loaf comes out clean. Let bread cool in pan for 10 minutes, then turn out onto a wire rack.
Notes
To enhance the flavor, you can add 1 teaspoon of vanilla extract or a pinch of cinnamon.