We study the electronic states of the magnetically ordered Mn3Pt alloy within the density functional theory. Mn3Pt has been believed that one third of Mn atoms have no magnetic moment in an antiferromagnetic phase (so-called the F-phase) realized in the temperature range of 400 K <T<475 K. We show that this experimentally suggested spin configuration is energetically so much unfavorable that it would be irrelevant to the F-phase. We discuss the possibility that the spin moments on the one third of Mn atoms are not paramagnetic but thermally fluctuating in the F-phase. The present results have an immediate connection with the recent neutron scattering study [T. Ikeda and Y. Tsunoda, J. Phys. Soc. Jpn., vol. 72, pp. 2614-2621, October 2003].