This is our second paper devoted to the problem of line intensity - oxygen abundance calibration starting from the idea of McGaugh (
1991ApJ...380..140M) that the strong oxygen lines ([OII] λλ3727, 3729 and [OIII] λλ4959, 5007) contain the necessary information to determine accurate abundances in HII regions. In the previous study (Pilyugin, 2000) the corresponding relations were obtained for the low-metallicity HII regions (12+logO/H≤7.95, the lower branch of the O/H-R
23 diagram). The high-metallicity HII regions (12+logO/H≥8.2, the upper branch of the O/H-R
23 diagram) are considered in the present study. A relation of the type O/H=f(P, R
23) between oxygen abundance and the value of abundance index R
23, introduced by Pagel et al. (
1979MNRAS.189...95P), and the excitation parameter P (which is defined here as the contribution of the radiation in [OIII] λλ4959, 5007 lines to the ``total" oxygen radiation) has been derived empirically using the available oxygen abundances determined via measurement of a temperature-sensitive line ratio [OIII]4959,5007/[OIII]4363 (T
e-method). By comparing oxygen abundances in high-metallicity HII regions derived with the T
e-method and those derived with the suggested relations (P-method), it was found that the precision of oxygen abundance determination with the P-method is around 0.1dex (the mean difference for the 38 HII regions considered is ∼0.08 dex) and is comparable to that of the T
e-method. A relation of the type T
e=f(P, R
23) between electron temperature and the values of abundance index R
23 and the excitation parameter P was derived empirically using the available electron temperatures determined via measurement of temperature-sensitive line ratios. The maximum value of differences between electron temperatures determined via measurement of temperature-sensitive line ratios and those derived with the suggested relation is around 1000K for HII regions considered here, the mean value of differences for 38 HII regions is ∼500K, which is the same order of magnitude as the uncertainties of electron temperature determinations in high-metallicity HII regions via measured temperature-sensitive line ratios.