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We have investigated the large magnetocaloric effect (MCE) in a Fe50.4Rh49.6 alloy subjected to a slowly cycled magnetic field of up to 1.8 T in magnitude over a range of temperatures, 250 K < T < 350 K. Our measurements showed that the MCE associated with the first order ferromagnetic/antiferromagnetic phase transition in this material was asymmetric with respect to whether the transition took place by heating the material from temperatures below the transition or by cooling it from above. We have explained these peculiarities using ab-initio density functional theory-based disordered local moment theory calculations.