Preheat oven to 350 degrees and grease a 9x5 loaf pan.

In a large bowl, mix together the flour, baking soda and salt.

In a different bowl, cream together the butter and brown sugar. Stir in eggs, vanilla and bananas until well blended.

Stir banana mixture into flour mixture, stir until just moistened.

Pour batter into loaf pan.

Bake for 60 minutes or until a toothpick comes out clean when inserted in the center. Let cool, then remove from pan.