Preheat the oven to 350 degrees F. In a medium bowl, combine the flour, baking soda, baking powder and salt. In a large bowl, cream together the eggs and sugar. Stir in the mashed bananas, vanilla, oil and cinnamon. Stir in the flour mixture, a third at a time, until just combined.
Pour the batter into a 9-by-5-inch loaf pan. Bake for about 1 hour.