Preheat the oven to 350°F (175°C). Grease and flour three 8-inch or two 9-inch cake pans.
Sift the flour, sugar, baking powder, baking soda, salt, and cinnamon into a large mixing bowl; add the shortening, buttermilk, and banana. Mix until all the dry ingredients are dampened, then beat at low speed for 2 minutes. Add the eggs and beat for 1 minute.
Divide the batter among the prepared pans and bake for 25 to 30 minutes. Cool for 10 minutes in the pans, then turn out the cakes on a rack to cool completely before frosting.