Preheat oven to 325 degrees.
In a separate bowl, measure and sift together the flour, baking soda and salt.
With an electric mixer, cream together the butter and sugar until soft and fluffy.
Add the eggs and vanilla and beat until well combined.
Add the mashed bananas and beat until well combined.
Add the flour mixture and mix well.
Add the chopped nuts and beat until well combined.
Place in a well greased loaf pan.
Bake at 325 degrees for 60 to 70 minutes, or until a toothpick insert comes out clean.
Allow loaf to cool slightly before transferring to a wire rack.