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Operating in the unlicensed 2.4 GHz ISM band, a Bluetooth piconet inevitably encounters interference problems from other piconets. With a special channel model and packet formats, one research issue is how to predict the packet collision effect in a multi-piconet environment. In an earlier work (A. El-Hoiydi, IEEE Comm. Ltrs., vol.5(6), p.245-247, 2001), this problem is studied, but the result is still very limited because it is assumed that packets must be single-slot ones and that the time slots of each piconet must be fully occupied by packets. These assumptions have been successfully removed in the analytical results proposed in (T. Lin et al, IEEE Comm. Ltrs., 2003). In this paper, we further improve these analytical results by taking into account the frequency-hopping guard time effect in the Bluetooth baseband. The results offer a way to better estimate the network performance in a multi-piconet environment.