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Climate change assessment, especially model evaluation, requires a better understanding of complex refractive indices (CRIs) of atmospheric aerosols - separately for both fine and coarse modes. However, the widely used aerosol CRI obtained by the global Aerosol Robotic Network (AERONET) corresponds to total-column aerosol particles without separation for fine and coarse modes. This paper establishes a method to separate CRIs of fine and coarse particles based on AERONET volume particle size distribution (VPSD), aerosol optical depth (AOD) and absorbing AOD (AAOD). The method consists of two steps. First a multimodal log-normal distribution that best approximates the AERONET VPSD is found. Then the fine and coarse mode CRIs are found by iterative fitting of AERONET AODs to Mie calculations. The numerical experiment shows good performance for typical water-soluble, biomass burning and dust aerosol types, and the estimated uncertainties on the retrieved sub-mode CRIs are about 0.11 (real part) and 78% (imaginary part). The 1-year measurements at the AERONET Beijing site are processed, and we obtain CRIs of 1.48-0.010i (imaginary part at 440 nm is 0.012) for fine mode particles and 1.49-0.004i (imaginary part at 440 nm is 0.007) for coarse mode particles, for the period of 2014-2015. Our results also suggest that both fine and coarse aerosol mode CRIs have distinct seasonal characteristics; in particular, CRIs of fine particles in winter season are significantly higher than summer due to possible anthropogenic influences.