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Bluetooth is a low-cost, low-power technology initially intended as a replacement of cables between electronic devices. Bluettoth devices can form small network of up to 8 devices called piconets. The specification also defines networks of piconets called scatternets. Scatternets can have various uses such as for "monitoring" purposes in factories and warehouses or for ad hoc meetings. Scatternets require the use of a routing scheme to find paths in a dynamic network. Though considerable research has been done in the area of routing in ad hoc networks, the direct application of this may be inefficient to Bluetooth scatternets. Some previous work has also presented routing schemes for scatternets, but this does not present any results showing the performance of the routing scheme. In this paper, we present a routing scheme for Bluetooth scatternets, which is based on the zone routing protocol. We motivate the design of the routing scheme keeping in mind the specifics of the Bluetooth technology. We present simulation results for the scheme, which show that the scheme gives very low overhead while keeping the route acquisition latencies low. The routing information at a node does not require a large amount of storage. In fact, a parameter in the scheme can be varied to trade-off storage information and routing overhead versus route acquisition latency.