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The source and relay precoders are jointly optimized for an amplify-and-forward multiple-input multiple-output relay system. Both the source and relay nodes employ orthogonal space-time block codes (OSTBC), and have imperfect channel state information of the source-relay and relay-destination channels, respectively. Using the worst-case robust design approach, we show that the problem of maximizing the minimum signal-to-noise ratio at the destination can be exactly reformulated as a convex optimization problem. Further, we provide an approximate semi-analytical approach which significantly reduces the computational cost of solving the convex problem. Numerical results show that this approximation is accurate and the proposed design outperforms OSTBC with eigen beamforming, OSTBC with equal power allocation, and currently available worst-case robust beamforming design without OSTBC.