Preheat oven to 350F.  Lightly grease a 9x5 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 to just moisten.

Pour batter into prepared loaf pan.  Bake in preheated oven 60-65 minutes until a toothpick inserted into center of loaf comes out clean.  Let bread cool in pan for 10 minutes, then turn out onto a wire rack.