Summary: In this paper we generalize the results obtained in [Publ. Math. 46, No. 3-4, 385-408 (1995; Zbl 0874.11013) and Publ. Math. 42, No. 3-4, 397-407 (1993; Zbl 0809.11008)] for the determination of the Hausdorff dimension of the univoque set. We break down the general problem into two subcases, and accomplish the investigation completely in the simplest case. Finally we illustrate the theoretical results with an interesting example.