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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 independently. In this letter, our first contribution is to incorporate the existing improvements into the original fast recursive algorithm to provide the fastest known algorithm for the optimal ordered SIC detection of V-BLAST. Subsequently, we propose two new algorithms that result from one further improvement for the fast recursive algorithm. Compared with the fastest known algorithm built from the existing improvements, one new proposed algorithm has a speedup of 1.3 times in both the number of multiplications and the number of additions, and the other new proposed algorithm requires less intermediate variables and saves memories.