This paper derives analytically an optimum amplifying relay matrix using the minimum mean square error (MMSE) criteria for a noncooperative amplify-and-forward (AF) distributed relay network. Global and local power constraints are included in the analysis. And a one-source-one-destination node pair and N-relay network is considered. Because the relays are noncooperative, this paper exploits the diagonal property in an amplifying relay matrix for the optimum matrix derivation. Then, this paper claims that the bit error rate of the AF network using the proposed amplifying relay matrix is significantly better than that of the AF network with the other existing amplifying matrices.