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Real-time multimedia streamings on the IEEE 802.11 wireless mesh networks will be one of the popular applications. It (802.11, WiFi) adapts an acknowledgement and retransmission mechanism to provide a reliable transmission environment. To perform the mechanism, the CRC-32 field will be required and attached behind the data frame. As the data frame becomes corrupt, it will be discarded and retransmitted. However, due to the time constraint, the retransmission may be not suitable for real-time streamings anymore. Thus, the CRC-32 field may be removed to reduce overhead of a data frame. As a result, the corrupt data frames can not be found by the intermediate mesh stations (mSTAs), and are still forwarded to the destination. The wireless bandwidth is wasted. Hence, a data frame should retain a low overhead error detection field. In this paper, we propose a successively computing CRC mechanism (SCCM) to generate the low overhead field for each data frame of real-time multimedia streaming in a wireless mesh network. The field adopts a partial CRC-32 checksum, but can possess efficient error detection ability. The SCCM performs the general CRC-32 calculation, it hence can be implemented on the current hardware circuit. Using the SCCM, the corrupt and useless data frames can be found and discarded in the network early. Thus, the mSTA resources and wireless bandwidth utilization can be improved significantly.