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In this paper, we propose a novel matrix inversion algorithm, which speeds up the corresponding step in the existing fast recursive algorithm for vertical Bell Laboratories layered space-time architecture (V-BLAST) by 1.67. Totally our improved recursive algorithm for V-BLAST speeds up the existing recursive algorithm for V-BLAST by 1.3. Furthermore, we develop an efficient recursive algorithm to implement the minimum mean- square error (MMSE) successive interference cancellation (SIC) detector with optimal ordering for Groupwise Space-Time Block Coded system (G-STBC), by exploiting the properties of the Alamouti structure in the equivalent channel matrix for G- STBC. Our recursive algorithm for G-STBC speeds up the low- complexity MMSE SIC algorithm with sub-optimal ordering for G-STBC by 2.57 approximately.