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A systematic straightforward network synthesis procedure using nullators and norators is presented. This procedure is derived by employing a theorem which gives sufficient conditions for networks containing nullators and norators to have a unique solution. These sufficient conditions are given in terms of the topological locations of the nullators and the norators with respect to the other elements in the network as well as their element values. These are used in the synthesis of admittance matrices. Results can be used in the synthesis of other types of matrices. It is shown that there exists a simple topology in the realization. Therefore the realization can be obtained directly, without going through the actual synthesis procedure.