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In this paper, a new analytical approach is developed for the evaluation of the outage probability of decode-and-forward (DF) automatic-repeat-request (ARQ) relaying under packet-rate fading (fast fading) channels. Based on this approach, a closed-form asymptotically tight (as SNR → ∞) approximation of the outage probability is derived, and the diversity order of the DF cooperative ARQ relay scheme is shown to be equal to 2L - 1, where L is the maximum number of ARQ retransmissions. The closed-form expression clearly shows that the achieved diversity is partially due to the DF cooperative relaying and partially due to the fast fading nature of the channels (temporal diversity). Numerical and simulation studies illustrate the theoretical developments.