We investigate the ionic rectifying effect through 4 and 20 nm thick silica nanochannels placed between two ionic solutions of different concentrations. The effect was observed when only a single side of the channel has electric double-layer overlap. The calculation based on Poisson-Nernst-Planck (PNP) theory and a simplified model suggests that the phenomenon result from the accumulation and depletion of both cations and anions in the nanochannels responding to different bias polarities. The model also elucidates that the basis of the rectifying effects in the nanofluidic devices reported to date is due to the asymmetric cation/anion ratios or equivalently built-in potentials on the two sides of the nanochannels. The study benefits the design of nanofluidic devices for attoliter-scale chemical delivery.