Development of new chemical nucleases is a matter of great interest because of their extensive use in biotechnology and as therapeutic agents. The ATCUN (amino terminal Cu(II) and Ni(II) binding) is a peptide motif that occurs naturally in the serum albumins. The similar peptide motif (GlyAibHis) having unnatural amino acid Aib (α- aminoisobutyric acid) was synthesized and its Cu(II) complex was characterized by ESI-MS and spectrophotometry studies. The reactivity of this complex toward DNA cleavage has been investigated. Cu(II)-GlyAibHis shows the DNA cleavage only in presence of mild oxidizing agents like ascorbate by an oxidative mechanism rather than hydrolytic and follows the pseudo first order kinetics (Kobs = 0.085 min-1). The non-hydrolytic mechanism was further supported by the hydrolysis of pNPP which followed the pseudo first order kinetics (Kobs = 1.98 x 10-2 min-1) having no pH effect.