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Broadcast is a fundamental operation in wireless sensor networks and plays an important role in the communication protocol design. This paper investigates the Minimum Latency Broadcast Scheduling in Duty Cycle (MLBSDC) problem in wireless sensor networks, which is known to be NP-hard. Recent studies in this area focus on giving collision-free scheduling and finding the upper bound of broadcast latency. The previously best-known algorithm for MLBSDC, OTAB algorithm, has an approximation ratio of 17|T| where |T| denotes the number of time slots in a working period. In this paper, we present an improved algorithm combining more transmissions into one working period, called Latency Aware Broadcast Scheduling (LABS) algorithm, to reduce the broadcast latency. Theoretical analysis proves that the LABS achieves the approximation ratio of 12|T| while keeping the same complexity with OTAB. We also conduct extensive simulations to show that our proposed algorithm achieves up to 34% and 40% performance improvement over existing schemes in terms of delay time and number of transmissions, respectively.