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A fast recursive algorithm for the vertical Bell Laboratories layered space-time (V-BLAST) with the optimal ordered successive interference cancellation (SIC) detection has been proposed by Benesty-Huang-Chen and two improved algorithms have been also recently introduced by Szczecinski-Massicotte and Zhu-Lei-Chin. In this paper, we first incorporate the existing improvements into the original fast recursive algorithm to give an algorithm that is the fastest known for the optimal SIC detection of V-BLAST. Then, we present a further improvement from which a new algorithm is proposed. Compared with the fastest known algorithm from the existing improvements, this new proposed algorithm has a speedup of 1.3 times in both the number of multiplications and the number of additions.