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We study the implementation algorithm for the MMSE-SIC detection with optimal detection order in a VBLAST system. We develop the LDLH decomposition based algorithm with backward substitution (LDBABS), which is shown to require as many multiplications as two other most efficient algorithms. We then propose a modified LDBABS algorithm that utilizes the scheme of incomplete LDLH decomposition together with the initial ordering information. The modified LDBABS algorithm is shown to require averagely fewer multiplications than any other implementation algorithm under the independent identically distributed Rayleigh fading channel. It is known that the real-valued MMSE-SIC detector with optimal detection order outperforms its complex-valued counterpart by approximately 1 dB. We finally propose a fast algorithm for the real-valued MMSE-SIC detector with optimal detection order. The number of real-valued multiplications required by this fast algorithm is approximately 1.57 times that required by the complex-valued LDBABS algorithm.