A to maximize sum rate (SR). Some of the solutions, especially the iterative ones, are capable of achieving very high performance. Nevertheless, they suffer from convergence problems. Closed form (CF) solutions on the other hand offer poor performances. This paper proposes a novel CF precoder design algorithm for the MU-MIMO BC, facilitated by stream selection. The proposed algorithm constructs the precoders per stream in a recursive manner. It contains two complementary steps: The first step consists in a recursive selection of the best available streams to minimize interference between users. This selection procedure is based on a null space criterion combined with the eigenvalues for each available stream. In the second step, the precoders are calculated according to the chosen precoding technique with eventually a power distribution optimization. Several precoding techniques can be applied, namely ZF (Zero Forcing) or MMSE (Minimum Mean Squared Error) linear beamforming (BF) and DPC (Dirty Paper Coding). We compare the proposed algorithm to some of the best CF algorithms available in the literature such as an all user SVD based recursive solution with ZF DPC precoders (ZFDPC-SUS). The obtained results demonstrate better performances for the proposed algorithm, closer to the sum capacity. We also show through a brief theoretical study that the SR of the proposed algorithm converges toward the DPC performance when the number of users grows to infinity.