  Simple relations for deriving the oxygen abundance in HII regions with
intensities of the three strong emission lines R_2, R_3, and N_2 (R
calibration) or S_2, R_3, and N_2 (S calibration) in their spectra are
suggested. A sample of 313 reference HII regions of the counterpart method is
used as calibrating data points. Relations for the determination of nitrogen
abundances, the R calibration, are also constructed. We find that the oxygen
and nitrogen abundances in high-metallicity HII regions can be estimated using
the intensities of the two strong lines R_2 and N_2 (or S_2 and N_2 for oxygen)
only. The corresponding two-dimensional relations are provided. There are
considerable advantages of the suggested calibration relations as compared to
the existing ones. First, the oxygen and nitrogen abundances estimated through
the suggested calibrations agree with the Te-based abundances within ~0.1 dex
over the whole metallicity range, i.e., the relative accuracy of the
calibration-based abundances is 0.1 dex. Although we constructed distinct
relations for high- and low-metallicity objects, the separation between these
two can be simply obtained from the intensity of the N_2 line. Moreover, the
applicability ranges of the high- and low-metallicity relations overlap for
adjacent metallicities, i.e., the transition zone disappears. Second, the
oxygen abundances produced by the two suggested calibrations are in remarkable
agreement with each other. In fact, the R-based and S-based oxygen abundances
agree within ~0.05 dex in the majority of cases for more than three thousand
HII region spectra.
