Preheat your oven to 350°F (175°C).
In a mixing bowl, combine flour, baking soda, and salt.
In another bowl, cream the butter and sugar until light and fluffy.
Beat in the eggs and vanilla extract.
Mix in the mashed bananas.
Alternate adding the flour mixture and buttermilk to the banana mixture, starting and ending with the flour mixture.
Pour the batter into a greased and floured cake pan.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.