  We suggest a new way to establish the relation between the electron
temperature t3 within the [OIII] zone and the electron temperature t2 within
the [OII] zone in high-metallicity (12+log(O/H) > 8.25) HII regions. The t2 -
t3 diagram is constructed by applying our method to a sample of 372 HII
regions. We find that the correlation between t2 and t3 is tight and can be
approximated by a linear expression. The new t2 - t3 relation can be used to
determine t2 and accurate abundances in high-metallicity HII regions with a
measured t3. It can also be used in conjunction with the ff relation for the
determination of t3 and t2 and oxygen abundances in high-metallicity HII
regions where the [OIII]4363 auroral line is not detected. The derived t2 - t3
relation is independent of photoionization models of HII regions.
