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We present a study of the structure and the corresponding magnetic property of Co5Ni95/Cu(001) ultrathin films during exposure to oxygen. For a film below the critical thickness (tc) of spin reorientation transition (SRT) from in-plane to a perpendicular direction, the SRT occurs while introducing oxygen for 25 Langmuir (L), followed by decreasing the perpendicular magnetization for further oxygen exposure. For a film above tc, the perpendicular magnetization is enhanced while introducing oxygen for 25 L and decreases during additional oxygen exposure. In both these cases, the interlayer distance (d) varies only 1.1% during the SRT or the enhancement of the perpendicular magnetization, whereas the d increases substantially when perpendicular magnetization disappears. This implies that the oxygen-induced SRT of the CoNi/Cu(001) alloy films is not materially affected by the d of the surface layer. This might indicate the formation of antiferromagnetic oxide that induces the SRT of CoNi/Cu(001) alloy films.