Preheat oven to 180 degrees C. Lightly grease a 13x23cm loaf tin.
In a large bowl, sift together flour, baking soda and salt. In a separate bowl, cream together butter and brown sugar. Stir in eggs and mashed bananas until well blended. Add banana mixture to flour mixture and stir just to moisten.
Pour batter into prepared tin and bake for 60 to 65 minutes, until a toothpick inserted into centre of the loaf comes out clean. Let bread cool in pan for 10 minutes, then turn out on to a wire rack.