Bluetooth is a low-cost, low-power wireless technology designed for establishing short-range radio links between portable devices in proximity. Exchanging multi-media namecards between portable devices and resource sharing among nodes in sights, constructing ad-hoc network in a personal area network are promising applications for a wireless proximity networking technology such as Bluetooth. Even if these kinds of applications are symmetrical in nature, the current Bluetooth specification requires an asymmetrical connection and its connection delay may be intolerably high. In this thesis, we propose a random inquiry procedure that allows a symmetrical user interface. Each party flips its state between the master and slave until a successful match is found. Through analysis, we find the optimal state transition strategy. Numerical results show that expected inquiry success time is about 30ms with optimal strategy, which is small enough to be used for namecard exchange. Moreover, we presents extended random inquiry scheme for multi-party random inquiry, named MURANI considering the case where the number of nodes that intend to be connected is unknown in random inquiry.