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Very recently, it was presented that the one dimensional (1D) CuO atomic chains can maintain large magnetic moments. In this work, we analyzed m-resolved density of states (DOS) to understand the peculiar spin polarization occurred in Cu atoms. It was found that the | m | = 1 states play an essential role in the spin polarization of Cu atoms. In addition, we calculated magnetic anisotropy energy (MAE) and observed that the distribution of MAE is strongly sensitive to the interatomic distance between Cu and O atoms. Besides, it was revealed that the contribution to MAE comes for the second half of Brillouin zone (BZ).