Preheat oven to 350°F. Spray an 8x4 inch loaf pan with nonstick spray.
In a medium bowl, whisk together the flour, baking soda and salt.
In a separate large bowl, use an electric mixer to combine the sugar and butter until well-blended. Add the eggs and mix in well. Add the banana, yogurt and vanilla; beat until blended. Add the dry ingredients and mix just until blended.
Scrape the batter into the prepared pan. Bake 50 to 60 minutes or until a toothpick inserted into the center comes out clean. Cool at least 20 minutes in the pan, and then turn out the loaf onto a rack to cool completely.