Preheat oven to 350°F (175°C). Lightly grease a 9x5 inch loaf pan.
In a large bowl, combine flour, baking soda, and salt.
In another bowl, cream together the butter and brown sugar until smooth.
Stir in the eggs and mashed bananas until well combined.
Gradually add the banana mixture into the flour mixture and stir just until moistened.
Pour the batter into the prepared loaf pan.
Bake for 60 to 65 minutes or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.