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In IEEE 802.16e WiMAX networks, burst is the system resource allocated by BS for users to receive or transmit data. Due to the limitation in system resource, designing an efficient way for BS to allocate the burst to MS becomes important. In general, burst allocation is regarded as the determination of the shape, location, and the modulation scheme of each burst, and it has been proved an NP problem. In this paper, we propose an efficient downlink bandwidth allocation scheme, namely EDBA, to allocate downlink bursts in a heuristic way. EDBA mainly considers the subchannel quality and selects a better modulation scheme for burst transmission to improve the subchannel utilization. Moreover, EDBA adjusts the shape and determines the location of the burst to reduce the numbers of unused slots (i.e., internal bandwidth wastage) and unallocated slots (external bandwidth wastage) resulted from the restriction of rectangular burst. The simulation results reveal that the proposed EDBA can achieve significant improvement in subchannel utilization and better network throughput than other mechanisms.