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In spectrum sharing systems, a secondary user (SU) is permitted to share frequency bands with a primary user (PU) as long as its transmission does not interfere with the PU's communication. In this paper, the outage probability is investigated for the cognitive relay system over Nakagami-m fading channel. By applying the interference temperature constraints at the source nodes and relay nodes in secondary systems, we analyze the outage performance in two-hop underlay spectrum sharing with the best relay selection criterion. The probability density function (PDF) and cumulative distribution function (CDF) of the signal to noise ratio (SNR) at the SU's receiver are derived to obtain the closed-form upper bound of the outage probability of the secondary relay system. Simulations results demonstrate the validity and accuracy of the theoretical analysis.