In multi user MIMO downlink with multi ante nnas at user terminals, the block diagonalization (BD) precoder obtains a bette r sum rate performance than matched filter (MF) and zero forcing (ZF), thus be comeing an attractive precoder. However, the conventional BD generates the null sp ace for all channel matrices excluding the current user by using s ingular value decomposition (SVD) and requires float point operations (FLOPs) o f order O(N2). As the antennas number N at ba se station (BS) tends to be a large scale one, computational complexity increas es sharply o n BS. Thus, a novel low complexity implementation for BD with a compl exity of order O(N) FLOPs is proposed, where the null space of other users′ c hannel matrices is constructed by a projection matrix. Simulation and ana lysis exhibit that the proposed low complexity BD significantly reduce the compl e xity, compared with the conventional BD and regularized block diagonalization(RB D) at the cost of a slight sum rate loss. The algorithm performs better than MF and ZF. Meanwhile, the sum rat e performance is similar to the conventional BD and SVD as N app roaches a large scale number.