This paper considers the circle map at the special point: the one at which there is a trajectory with a golden mean winding number and at which the map just fails to be invertable at one point on the circle. The invariant density of this trajectory has fractat properties. Previous work has suggested that the global behavior of this fractal can be effectively analyzed using a kind of partition function formalism to generate an f versus a curve. In this paper the partition function is obtained by using a renormalization group approach.