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This paper proposes a modified sorted-QR decomposition algorithm for the high-dimensional multiple-input multiple-output (MIMO) detection. Due to the growing demands of high-dimension MIMO channels and large number of OFDM subcarriers, the sorted-QR decomposition becomes one of the computational bottlenecks in the QR-based MIMO detection. The proposed Givens-rotation-based algorithm aims to improve the throughput and the hardware utilization efficiency by relaxing the sorting condition and allowing the cross-column parallel rotation operations. The simulation results show that our proposed parallel algorithm can significantly reduce the minimal computation latency from 28% to 21% of the original algorithm, and the hardware utilization rate can be enhanced from 71% to 90% for 16times16 MIMO using four Given-rotation processing elements. The detection performance degradation is negligible and better hardware efficiency can be obtained for the larger number of MIMO antennas.