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The choice of a ”good” interleaver in IDMA systems must demonstrate that the interleavers do not ”collide” and easy to generate. In this paper, we develop a new one-dimensional system, completely based on the logistic map: ”New Logistic Map (NLM)”. We use the NLM to generate an interleaver matrix for IDMA systems: NLM Interleaver. The simulation results of chaotic dynamical behaviours show that the NLM is a chaotic system and has an ideal distribution. It is also characterized by its wide range of definition, and depends on the number of the desired real values. In addition, the correlation performances of NLM Interleaver are the same as those found in the literature for different interleaver designs.