In multiuser multiple-input multiple-output (MU-MIMO) wireless downlink systems, block diagonalization (BD) is a technique, where the transmit precoding matrix of each user is designed such that its subspace lies in the null space of all the other remaining users, so that multiuser interference (MUI) is completely canceled. In low signal to noise power ratio (SNR) or low signal to interference plus noise power ratio (SINR) environments, regularized BD, that lets some MUI remain and maximizes the sum rate capacity of the BD MIMO channel, was also proposed. One of the problems of both the approaches is high complexity of computation due to a lot of singular value decomposition (SVD) processes. In this paper we propose new BD techniques utilizing QR decomposition (QRD) which can be practically achieved by Gram-Schmidt orthogonalization (GSO) with lower complexity compared to the conventional method employing SVD. We can show that the performance of the proposed approaches is close to the conventional approaches, while the proposed approaches have much lower complexity.