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)over cap, the calculation results show that the capacity-based algorithm has 4(K)over cap 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.