A non series-parallel system of (m, ,l) orderis designed by taking ‘m’ parallel subsystems each containing components connected in series. And, the ‘l’ additional componentsare linked to arbitrary non-adjacent  and  components ofeach parallel subsystem. The use of Logic Diagram Technique (LDT) has been made to determine the possible number of maximum effective duplication paths due to additional components. The duplication paths which include other paths are discarded keeping in view of the fact that these paths haveno effect on reliability of the system. The expressions for reliability and mean time to system failure (MTSF) are derived in general form by assuming exponential failure laws of the components using Path Tracing Method (PTM). The system reliabilityis evaluated for arbitrary values of the failure rate of the components of each subsystem, failure rate of the additional components and the number of additional components. An illustration is given to see the effect of various parameters on system reliability. The possible application of the present study has been discussed as an example of Power Distribution System.