This paper proposes a new receive antenna selection algorithm based on the theory of convex optimization that improve the system performance over Rayleigh fading multiple-input multiple-output (MIMO) channels. The algorithm is based on approximated relaxed original optimization problem. The main effort in the approximated relaxed method is computing the Newton step for the centering problem, which consists of solving sets of linear equations constraints. The method produces not only a suboptimal choice of receive antennas, but also, a bound on how well the globally optimal choice does. The Monte-Carlo simulations show that the algorithm proposed can provide the performance very close to that of the optimal selection based on exhaustive search.