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In this paper, we present the algorithm and the results of a modified support vector machine (SVM) detector on a Chaos-based code division multiple access (CDMA) system so that it has less computational complexity than the conventional correlator receiver. This is achieved through the recursive feature elimination (RFE) algorithm, which is commonly used for feature extraction in bioinformatics applications. The system was simulated under both AWGN and Rayleigh fading channels. Simulation results showed that the modified scheme has less complexity than the conventional correlator and provides a much better BER performance. The maximum performance loss is only 2 dB away from a standard SVM detector under AWGN and no significant difference was observed under the Rayleigh fading channel.