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The fixed-complexity sphere decoder (FSD) has been proposed to attain the near-optimal performance achieving the same diversity order as the maximum-likelihood decoder (MLD) recently. However, it suffers great redundant computations resulting in high power consumption. In this paper, we conduct an improved algorithm for the original FSD by using early termination (ET). This algorithm (abbreviated as ET-FSD) preserves the advantages of sphere decoder (SD) such as branch pruning and an adaptively updated pruning threshold. We compare the ET-FSD with the original FSD and a lately developed statistical threshold-based FSD (ST-FSD). Simulation results demonstrate that the ET-FSD attains the same performance with a much lower cost than the FSD, and is much more efficient than the ST-FSD in practice. In addition, the statistical threshold-based method can also be used for the ET-FSD (i.e., ST-ET-FSD) to further reduce the complexity.