The C IV...1498,1501 broad emission line is visible in optical spectra to redshifts exceeding z ~ 5. C IV has long been known to exhibit significant displacements to the blue and these 'blueshifts' almost certainly signal the presence of strong outflows. As a consequence, single-epoch virial black hole (BH) mass estimates derived from C IV velocity widths are known to be systematically biased compared to masses from the hydrogen Balmer lines. Using a large sample of 230 high-luminosity (LBol = 10...-10... erg s...), redshift 1.5 < z < 4.0 quasars with both C IV and Balmer line spectra, we have quantified the bias in C IV BH masses as a function of the C IV blueshift. C IV BH masses are shown to be a factor of 5 larger than the corresponding Balmer-line masses at C IV blueshifts of 3000 km s... and are overestimated by almost an order of magnitude at the most extreme blueshifts, ...5000 km s... Using the monotonically increasing relationship between the C IV blueshift and the mass ratio BH(C IV)/BH(Ha), we derive an empirical correction to all C IV BH masses. The scatter between the corrected C IV masses and the Balmer masses is 0.24 dex at low C IV blueshifts (~0 km s...) and just 0.10 dex at high blueshifts (~3000 km s...), compared to 0.40 dex before the correction. The correction depends only on the C IV line properties -- i.e. full width at half-maximum and blueshift -- and can therefore be applied to all quasars where C IV emission line properties have been measured, enabling the derivation of unbiased virial BH-mass estimates for the majority of high-luminosity, high-redshift, spectroscopically confirmed quasars in the literature. (ProQuest: ... denotes formulae/symbols omitted.)