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In this paper, a new equivalent relay channel model is developed for analyzing the error performance of detect-and-forward (DetF) relay networks and is compared to the minimum equivalent relay channel model typically used in DetF systems. The considered cooperative relay network comprises two users, single destination, 4-ary Galois field (GF(4)) network coded, QPSK modulated, DetF in a flat Rayleigh fading environment. The destination performs maximum likelihood (ML) decoding utilizing the error rates of the source-relay links. Pairwise error probability results show that the proposed equivalent channel model sucessfully approximates the relay channel.