Recently, bluetooth technology has become widely prevalent so that many laptops and mobile phones are equipped with bluetooth capability. In order to meet the increasing demand to interconnect these devices a new scatternet formation protocol named GBSFP (General Bluetooth Scatternet Formation Protocol) is proposed in this paper. GBSFP is the result of efforts to overcome the two major limitations of the legacy scatternet formation protocols as regards their real implementation, that all of the nodes should be within the Bluetooth communication range or that they should be time synchronized. In GBSFP, a node goes through three phases; 1) the Init phase to establish a bluetooth link to as many of its neighbors as possible, 2) the Ready phase to determine the role of each node, i.e., master or slave, and remove any unnecessary bluetooth links, and 3) the Complete phase to finalize the formation of the scatternet and begin data transmission. The simulation results show that GBSFP provides higher connectivity in many scenarios compared with BTCP and BlueStars.