Resolution-enhancement software and first-principles calculation for electron energy-loss spectroscopy (EELS) were applied for the study of aluminium (Al) coordination in alumina. Al-L23 energy-loss near-edge structures (ELNES) of alpha- and gamma-aluminas were observed using a field-emission transmission electron microscope and advanced software for EELS. The inherent energy resolution of a cold field-emission gun (FEG) of approximately 0.3 eV was realized using drift-correction software. The energy spread of the cold FEG was deconvoluted by means of maximum-entropy or Richardson-Lucy algorithms and the energy resolution of the deconvoluted spectrum became comparable with that obtained using a monochromator, whose energy resolution was < 0.2 eV. Fine structures in Al L23-edge were observed, such as 0.5 eV splitting between L3 and L2 peaks in alpha-alumina (i.e. spin-orbit splitting). The difference in Al coordination was clearly observed in Al-L23 ELNES and the major structures near the threshold were assigned using first-principles calculations.