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This paper proposes a new transmit power allocation (TPA) scheme for the vertical bell layered space time (V-BLAST) system with zero-forcing ordered successive interference cancellation (ZF-OSIC) detection. The proposed TPA scheme is based on the minimization of the average probability of vector error subject to a constraint on the total average transmitted power. To derive the TPA algorithm, we consider the asymptotic approximation of the average probability of vector error that is valid at high signal-to-noise ratio. The resulting TPA scheme allocates powers to the transmit antenna elements considering very limited feedback from the receiver. Computer simulations are used to demonstrate the effectiveness of the proposed approach for a V-BLAST system with a maximum of four transmit and receive antenna elements.