In dual-hop relaying systems, the conventional partial relay selection is based on the channel information only for the first hop. On the other hand, the efficient partial relay selection is based on the channel information for the hop with the minimum of the average channel powers for the first and second hops at each end-to-end link since the correlation coefficient between the end-to-end link quality and the link quality of the hop with the minimum of the average channel powers for the first and second hops is larger than that between the end-to-end link quality and the link quality of the other hop. In this paper, the outage probability of the conventional partial relay selection and the efficient partial relay selection in dual-hop decode-and-forward relaying systems is analyzed for non-identically distributed Rayleigh fading channels. Through numerical investigation, the outage performance of the efficient partial relay selection is compared with the outage performances of the conventional partial relay selection and the best relay selection based on all the channel information for the first and second hops.