In a small saucepan, stir together sugar and water. Bring to a boil, then remove from heat and allow to cool.
When the sugar syrup is cool, stir in bananas.
Pour into a freezer - safe baking dish. Freeze for 3 to 4 hours, until set at the edges.
Remove from the freezer and transfer to a mixing bowl. Use an electric mixer to beat until smooth. Return to the freezer until gently set, at least 2 hours.
