  The CIV broad emission line is visible in optical spectra to redshifts
exceeding z~5. CIV 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 CIV velocity-widths are known to be systematically biased compared
to masses from the hydrogen Balmer lines. Using a large sample of 230
high-luminosity (log $L_{\rm Bol}$ = 45.5-48 erg/s), redshift 1.5<z<4.0 quasars
with both CIV and Balmer line spectra, we have quantified the bias in CIV BH
masses as a function of the CIV blueshift. CIV BH masses are shown to be a
factor of five larger than the corresponding Balmer-line masses at CIV
blueshifts of 3000 km/s and are over-estimated by almost an order of magnitude
at the most extreme blueshifts, >5000 km/s. Using the monotonically increasing
relationship between the CIV blueshift and the mass ratio BH(CIV)/BH(H$\alpha$)
we derive an empirical correction to all CIV BH-masses. The scatter between the
corrected CIV masses and the Balmer masses is 0.24 dex at low CIV 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 CIV line
properties - i.e. full-width at half maximum and blueshift - and can therefore
be applied to all quasars where CIV emission line properties have been
measured, enabling the derivation of un-biased virial BH mass estimates for the
majority of high-luminosity, high-redshift, spectroscopically confirmed quasars
in the literature.
