The lateral diffusion of nano-meter-sized constituents (proteins, lipid rafts and so on) in lipid bilayers is of biological interest because the biochemical functions may be diffusion controlled. Saffman and Delbruck (SD) dealt with this issue using a hydrodynamic theory and derived an expression of the diffusion coefficient D forsmall domain size limit as D(r)=kBT[ln(ηmh/ηmr)-0.0773]/4πηmh, where ηm and ηw are the viscosities of the membrane and the aqueous phase, respectively, h is the membrane thickness, r is the radius of the diffusing object. In this study we addressed the SD model by direct measurement of the intermediate scattering function of the nano-meter-sized liquid ordered domains in the fluid membrane using a contrast matching technique of neutron spin echo. We prepared ternary small unilamellar vesicles (SUVs) composed of deuterated DPPC, hydrogenated DOPC, hydrogenated cholesterol. The obtained intermediate scattering functions for the phase separated SUVs were fitted by a double exponential function, S(q,t)/S(q,0)=Aexp(-D0q2t)+(1-A)exp(-(D0+Dd)q2t), where A is the numerical constant, D0and Dd are the diffusion coefficients of whole SUV and nano-meter sized domain, respectively. The fitting of S(q,t)/S(q,0) gave Dd = 2.3 x 10−12 m2/s, where the domains have the mean radius of 7.5 nm. The obtained domain diffusion coefficient agrees well with the SD prediction of D= 2.35 x 10−12 m2/s using Ns/m2 and Ns/m2. Furthermore, by combining present data with the diffusion coefficient of a DPPC single molecule in Ld phase of DDPPC ≈ 3.5 x 10−12 m2/s, we clearly demonstrates that the SD model well describes the observed diffusion coefficients in nano-meter length scale.