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Detection of transmitted symbols in a V-BLAST system using the minimum mean squared error criterion with successive interference cancellation (MMSE-SIC) can provide satisfactory bit error rate performance at the cost of moderate computational complexity. The fast recursive algorithm (FRA), developed by Benesty et al., is one of the well-known implementation algorithms for the MMSE-SIC detector. We modify the FRA to compute an ordered set of nulling vectors from the estimated channel information. Our modified FRA can be used with the transformation based successive interference cancellation procedure to process a V-BLAST frame that contains the preamble and payload. To our knowledge, such implementation of the MMSE-SIC detector requires the lowest complexity to process a frame of preamble and payload.