The reaction of O(D-1) with N2O produces two kinds of NO molecules, the "old" one which originally exists in N2O and the "new" one which includes the attacking O atom. Using the isotopically labeled reagent, we determined the vibrational state distributions of these NO's (X (2)Pi; v=0-17) separately. To obtain the distributions, two types of experiments were performed with the laser-induced fluorescence (LIF) technique via the NO A<--X and B<--X transitions. First, the relative populations of NO molecules (the sum of the two kinds of NO's) in v=0-11 levels were measured with unlabeled reagents. Then, isotopically labeled reaction, O-18(D-1)+(N2O)-O-16-->(NO)-O-18+(NO)-O-16, was utilized to determine the relative ratio between the two kinds of NO's in the vibrational levels of v=0-5 and 12-15. Combining the above results with previously determined vibrational state distribution of NO in high vibrational levels (v=11-17) [J. Chem. Soc., Faraday Trans. 94, 1575 (1998)], we were able to obtain a complete set of vibrational state distributions. It was found that the old NO dominantly populated in v=0 and 1 whereas the new NO extended its population toward higher vibrational levels (v=4-15). However, in high vibrational levels, the old NO still have a considerable population due to the rapid energy transfer to the old NO. The observed efficient energy transfer to the old NO is attributed to the absence of light atoms in the present reacting system. Compared with the system including hydrogen atoms, the state density and the momentum coupling among the vibrational modes are much larger and accelerate the energy redistribution in spite of the short lifetime.