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Various burst construction algorithms for Orthogonal Frequency Division Multiple Access (OFDMA) were proposed. However, these algorithms did not consider the downlink burst characteristics that are specified in IEEE 802.16 standard. This work therefore presents the Best Block-Oriented (BBO) algorithm. BBO not only complies with the downlink burst characteristics, but also addresses three further issues that are important to obtain high throughput: BBO reduces external fragment by shrinking a burst to fit into the available bandwidth area if the available area is otherwise insufficient to accommodate it; BBO shrinks the burst area to minimize internal fragment if the requested bandwidth has been satisfied; to find the subchannels that have good channel quality, BBO evaluates the channel quality of subchannels and constructs the burst in the subchannels that provide the highest throughput. Simulation results show that BBO yields 1.2-9 times the throughput that has been achieved using previous algorithms under a heavy load.