Peel the bananas and place them in a large mixing bowl before mashing them with the back of a fork.
Continue to mash until smooth, then add half a cup of caster sugar.
Add one cup of mayonnaise to the banana and sugar mixture.
Sieve in the two cups of self-raising flour and stir everything together until blended into a pale yellow mixture.
Take a standard-sized loaf tin, grease lightly with butter, and line it with greaseproof paper, allowing some overhang of the paper over the sides.
Heat the oven to 180C and pour the batter into the prepared loaf tin.
Bake for 40 minutes or until cooked through.