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The influence of quenching temperature, heating atmosphere and annealing time on superconducting characteristics has been studied for LuBa2Cu3O7-z compound which has been recently synthesized in a nearly phase-pure form. Resistivity measurements for the as-prepared sample heated at 300 °C in oxygen and subsequently quenched into liquid nitrogen revealed that there is no significant change in Tc. On the other hand, Tc of the sample slightly increased when the sample was heated at 300 °C either in air or in N2 atmosphere. It was also found that Tc of the sample decreased when the annealing temperature in N2 atmosphere increased above 400 °C. The experimental results indicated that the as-prepared sample is under overdoped state. The enhanced superconducting transition observed in the samples after heating at 300 °C in air or N2 atmosphere was discussed in conjunction with a slight removal of oxygen and ordering of oxygen atoms in the as-prepared sample.