In an attempt to remove the systematic errors which have plagued the calibration of the Hii region abundance sequence, we have theoretically modelled the extragalactic Hii region sequence. We then used the theoretical spectra so generated in a double-blind experiment to recover the chemical abundances using both the classical electron temperature + ionization correction factor technique and the technique which depends on the use of strong emission lines (SELs) in the nebular spectrum to estimate the abundance of oxygen. We find a number of systematic trends, and we provide correction formulae which should remove systematic errors in the electron temperature + ionization correction factor technique. We also provide a critical evaluation of the various semi-empirical SEL techniques. Finally, we offer a scheme which should help to eliminate systematic errors in the SEL-derived chemical abundance scale for extragalactic Hii regions.