Enormous capacity advantage can be achieved on a flat MIMO channel compared to single antenna systems. V-BLAST was proposed to obtain such capacity advantage with low complexity. V-BLAST, however, requires multiple matrix (pseudo) inversions that are still computationally intensive for a large number of antennas. Much research has been attracted to reducing the complexity. Our contribution is to show that the MMSE block decision-feedback equalizer equivalent to the MMSE V-BLAST can be calculated via Cholesky factorization of the error covariance matrix with symmetric permutation. Forward and backward filters as well as detection order are jointly optimized with significantly reduced complexity. Simulation results show that MMSE V-BLAST performance can be achieved by the proposed scheme.