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In this paper, we present a scalable, decentralized task allocation algorithm for a group of unknown number of unmanned aerial vehicles (UAVs), which are equipped with GPS receivers, synchronized clocks and radars with a finite, but known operating distance to identify neighbors. The algorithm assigns subgroups of UAVs, whose initial positions are randomly scattered in a bounded space, to a finite set of independent tasks. The key features of the proposed algorithm are: (1) the algorithm does not require any communication between the UAVs; (2) the task allocation is achieved in finite time. The analysis and results in the simplified 2D simulation environment respectively prove and verify the correctness of the proposed algorithm.