The basic structure of alpha-LiFeO2, lithium iron oxide, is a cubic NaCl-type structure with a lattice constant of 0.42 nm; some short-range ordering characterized by octahedral clusters exists. The local structure of the short-range ordering was investigated by transmission electron microscopy and electron diffraction. A new short-range ordering structure was found in local areas. The local structure has a cubic lattice with a doubled lattice constant. The occupation factors of cations on Wyckoff sites 4(a) and 4(b) are different from those on 24(d) sites, but the stoichiometric composition in cubic clusters is the same as the macroscopic composition. The number of pairs in which iron cations exist in nearest-neighbor sites and next nearest-neighbor sites is reduced in the structure. This means that a magnetic interaction between the iron cations is reduced by cation ordering even without spin ordering at room temperature.