Preheat the oven to 350*.
Combine the flour, baking soda, salt, sugar, and butter in a large mixing well.
Add in the eggs and mix well.
Add in the banana, ½ cup shredded wheat, and vanilla.
Grease a 9-inch loaf pan and spoon batter into it, spreading it evenly.
Top it with the reserved shredded wheat.
Bake for 1 hour at 350* or until when poked with a toothpick in the deepest part it comes out clean.
Cool and carefully remove from pan.
