We report a model for the explanation of the single molecule magnet behavior of the [CuIILTbIII(hfac)2]2 cluster. The model takes into account the crystal field acting on the Tb III -ion and the exchange interaction between the TbIII and CuII ions. The energies of the low-lying levels are shown to increase with the decrease of the mean value of the z-projection of the total angular momentum of the cluster, thus forming a barrier for magnetization reversal that is in accordance with the experimental evidence.