We studied the mechanism of the N+NO reaction on Rh(111) surfaces by means of fast near-edge X-ray absorption fine structure spectroscopy. This reaction is important as a basis of NOx reduction reactions on platinum-group metal surfaces. Atomic nitrogen layers on Rh(111) were titrated with NO at various temperatures. N2O is exclusively formed and desorbs into the gas phase below 350 K. The consumption rate of atomic nitrogen exhibits strange temperature dependence between 100 and 350 K; the reaction proceeds slower with increasing temperature. Reaction kinetics analyses and isotope-controlled experiments have revealed that the surface N atoms do not react with chemisorbed NO molecules but with NO dimers weakly bound on top of the chemisorbed layer, which play a role as an extrinsic precursor. The present results may support the possibility that NO dimers participate in various NO-related synthetic, biochemical, and surface reactions as an intermediate.