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A new volume-based user selection algorithm with low complexity is proposed for a multiuser multiple-input and multiple-output downlink system based on block diagonalisation precoding. The new algorithm achieving this reduced computational complexity is compared with other user selection algorithms, such as semi-orthogonal user selection (SUS) and capacity-based user selection algorithms. The proposed algorithm stems from the new volume-based user selection method that uses the product of the diagonal elements in the upper-triangular matrix obtained via Householder reduction procedure of QR factorisation to the selected users channel matrix. The computational effort of the new algorithm is reduced by one-fourth compared with SUS algorithm. Compared with the capacity-based algorithm, the proposed algorithm does not need to perform the singular value decomposition operation and water-filling algorithm during each user selection step, and hence, significantly reduces the computational time. If the maximum number of supportable users is K, the calculation results show that the capacity-based algorithm has 4K times the complexity of the proposed algorithm. Furthermore, the simulation results demonstrate that the volume-based algorithm displays better capacity performance than the SUS algorithm, and the sum-rate capacity of the volume-based algorithm is comparable with that of the capacity-based algorithm but with much less computational complexity.