Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch square baking dish.
Beat butter and sugar with an electric mixer in a large bowl until light and fluffy; beat in eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Stir bananas into butter mixture.
Sift flour, baking soda, and salt together in another bowl. Stir flour mixture into banana mixture until batter is evenly blended.
Pour batter into prepared baking dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes.
