Recently, efficient partial relay selection (e-PRS) was proposed as an enhanced version of PRS. In comparing e-PRS, PRS, and the best relay selection (BRS), there is a tradeoff between complexity and performance; that is, the complexity for PRS, e-PRS, and BRS is low to high, respectively, but vice versa for performance. In this paper, we study the outage probability for e-PRS in decode-and-forward (DF) relaying systems over non-identical Nakagami-m fading channels, where the fading parameter m is an integer. In particular, we provide closed-form expressions of the exact outage probability and asymptotic outage probability for e-PRS in DF relaying systems. Numerical results show that e-PRS achieves similar outage performance to that of BRS for a low or medium signal-to-noise ratio, a high fading parameter, a small number of relays, and a large difference between the average channel powers for the first and the second hops.