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A performance analysis for cooperative diversity system with best relay selection over Rayleigh fading channels is presented. We obtain analytical expressions for the probability density function (PDF), cumulative density function (CDF), and the moment generating function (MGF) of end-to-end SNR of the system under study. Using these expressions we derive closed-form expressions for the average symbol error rate (SER), the outage probability and the average end-to-end SNR gain obtained form relay selection. Using numerical simulations and calculation of the mathematical expressions, the performances of different cases are evaluated and compared to show the significant advantages of the relay selection in a cooperative communication.