Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 7x3-inch loaf pans.
Whisk flour, sugar, baking soda, and salt together in a bowl. Mix in melted butter and beaten eggs, then stir in mashed bananas. Pour batter into the prepared pans.
Bake in the preheated oven until a wooden toothpick inserted into the center comes out clean, about 1 hour.