Preheat oven to 350 degrees.
Sift together flour, salt, and baking soda. Set aside.
Melt butter on the stove or in the microwave. Mix butter and sugar until well blended. Add eggs, one at a time, mixing well after each. Add bananas and vanilla. Fold in flour mixture and walnuts and blend until all flour is moist.
Grease 2 loaf pans and divide batter equally between the 2 pans. Bake for 1 hour or until center of loaf is firm and a toothpick inserted in center comes out clean.