Bluetooth is becoming a promising way to be employed for wireless personal area networks (WPANs). In a Bluetooth network, a good scatternet topology is an important issue since it can reduce the routing overhead and improve the overall network performance. The paper proposes a novel distributed algorithm, Group-Scatternet Formation Algorithm (GSFA), to construct a Bluetooth scatternet. GSFA consists of two phases, piconet formation and group-scatternet formation. The resulting scatternet is connected and robust due to the existence of multiple paths between any two Bluetooth devices. Additionally, based on the resulting scatternet, we also develop a new routing protocol, by which route search packets need not to be flooded all over the network while a source is looking for a route path to the destination. A lot of simulations are performed to verify the performance of GSFA and the resulting scatternet. The experimental results show that three groups are suitable for the network with less than 50 devices, while two groups are preferred when the number of devices exceeds 50. We also validate the performances of the proposed method by comparing GSFA with three different approaches, BTCP, LINEAR, and Tree-based approaches. The results show the advantages of the proposed method. Especially, the scatternet generated by GSFA is good at low packet delay and high network throughput.