In a large bowl, mix together flour, sugar, baking soda, and salt.
In another bowl, combine the eggs, bananas, oil, buttermilk, and vanilla;
Add to flour mixture, stirring just until combined.
Fold in nuts.
Pour into a greased 9 by 5 in. loaf pan. Bake at 325 for 1 hour and 20 minutes or until a toothpick comes out clean. Cool on wire rack. Yield one loaf.