The ATIC balloon-borne experiment measures the energy spectra of elements from H to Fe in primary cosmic rays from about 100 GeV to 100 TeV. ATIC is comprised of a fully active bismuth germanate calorimeter, a carbon target with embedded scintillator hodoscopes, and a silicon matrix that is used as a main charge detector. The silicon matrix produces good charge resolution for the protons and helium but only a partial resolution for heavier nuclei. In the present paper a charge resolution of ATIC device was essentially improved and backgrounds were reduced in the region from Be to Si by means of the upper layer of the scintillator hodoscope that was used as an additional charge detector together with the silicon matrix. The flux ratios of nuclei B/C, O/C, N/C in the energy region from about 10 GeV/nucleon to 300 GeV/nucleon that were obtained from new high-resolution and high-quality charge spectra of nuclei are presented. The results are compared with existing theoretical predictions