Preheat oven to 350 degrees. Grease a standard loaf pan with a little extra light olive oil.
In a large bowl beat together the oil and sugar until blended. Beat in the banana, then the eggs until completely mixed. Add the flour, baking soda and salt. Be careful to not over mix. Stir in the walnuts with a spatula just until blended.
Spread the mixture into the loaf pan and bake for 50-60 minutes, or until a toothpick inserted in the center of the loaf comes out clean. Cool in the pan for about 15 minutes, then turn onto a wire rack to cool completely.