Preheat the oven to 350 degrees F. Grease a 9x5x3-inch loaf pan and line the bottom with parchment; set aside.
In a medium bowl, blend flour, baking soda, cinnamon, and salt. Set aside.
In a large bowl, combine sugar, oil, eggs, and vanilla; stir briskly with a rubber spatula until combined. Stir in mashed bananas and yogurt. Add flour mixture and stir until batter is well combined. Spread evenly into the prepared loaf pan.
Bake for 50 minutes, or until an inserted toothpick comes out clean. Cool loaf in the pan for 20 minutes, then remove loaf to a wire rack to cool completely.