This paper proposes a novel closed form (CF) precoder design for multi-user multiple input multiple output broadcast channel (MU-MIMO BC). The proposed algorithm is based on Null Space Zero-Forcing or Null Space Zero-Forcing with Greedy Stream Selection. The idea is to construct the precoder in a recursive stream-wise manner. The design proceeds in two steps. The first step is a recursive selection of the best streams, under a zero-forcing (ZF) constraint. The selection is based on an extension of Gram-Schmidt orthogonalization for the MIMO channel case, involving SVDs (geared towards per stream DPC). The streams associated to the strongest singular values get selected. In a second step, the precoder for the selected streams are calculated according to one among several possible precoding techniques with eventually a power distribution optimization. The proposed algorithm is then compared to the best algorithms in the literature namely the ZFBF-SUS and to it's DPC version ZFDPC-SUS. The obtained results showed better performances closer to DPC.