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In this paper, the performance of multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) relay systems using orthogonal space-time block codes (OSTBCs) over arbitrarily correlated Nakagami- m fading channels is analyzed. In particular, closed-form expressions for the end-to-end outage probability (OP) and the symbol error probability (SEP) with arbitrary number of transceiver antennas and general correlation matrices are derived. Their mathematically tractable forms readily enable us to evaluate the performance of MIMO AF relay systems that utilize OSTBCs. For sufficiently high signal-to-noise ratios (SNRs), asymptotically tight approximations for the OP and SEP are also attained, which reveal insights into the effects of fading parameters and antenna correlation on the system's performance. Furthermore, we prove that the correlation has no impact on the achievable diversity gain, which is equal to the minimum of the sum of fading parameters between the two hops. Selected numerically evaluated results are presented, showing an excellent agreement between the proposed analysis and equivalent Monte Carlo simulations.