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The use of biomedical sensor networks in complex clinical diagnostics and treatment may provide greater flexibility for both patient and the medical staff as some of the same sensors could follow the patient throughout the cycle of treatment. Biomedical sensors usually transmit periodically with known intervals and may require medium to higher data rates and lower packet drop rate than most traditional sensor networks. We propose a new method built on the IEEE 802.15.4 standard to enable higher throughput while keeping the packet drop rate at a minimum by utilizing the periodic behavior observed in such sensor networks. The simulation results show that, for certain scenarios, the average throughput compared to the IEEE 802.15.4 standard configuration can be doubled, while keeping the packet drop ratio at a minimum. Furthermore, by utilizing the property of periodic behavior, the channel efficiency has been improved from 30% to 50% compared to the standard IEEE 802.15.4 configuration. We show that the proposed method generates less protocol overhead and significantly reduces the chance of transmission errors due to colliding packets. Thus, it attains operational performance closer to saturation for a given packet discard ratio. Energy consumption due to retransmissions is reduced as the proposed algorithm greatly reduces collisions and requires few retransmissions. The proposed method requires minimum computational complexity and can be used on sensor nodes in a decentralized manner.