  We aim to obtain a complete sample of redshift > 3.6 radio QSOs from FIRST
sources having star-like counterparts in the SDSS DR5 photometric survey
(r<=20.2). We found that simple supervised neural networks, trained on sources
with SDSS spectra, and using optical photometry and radio data, are very
effective for identifying high-z QSOs without spectra. The technique yields a
completeness of 96 per cent and an efficiency of 62 per cent. Applying the
trained networks to 4415 sources without DR5 spectra we found 58 z>=3.6 QSO
candidates. We obtained spectra of 27 of them, and 17 are confirmed as high-z
QSOs. Spectra of 13 additional candidates from the literature and from SDSS DR6
revealed 7 more z>=3.6 QSOs, giving and overall efficiency of 60 per cent. None
of the non-candidates with spectra from NED or DR6 is a z>=3.6 QSO,
consistently with a high completeness. The initial sample of z>=3.6 QSOs is
increased from 52 to 76, i.e. by a factor 1.46. From the new identifications
and candidates we estimate an incompleteness of SDSS for the spectroscopic
classification of FIRST 3.6<=z<=4.6 QSOs of 15 percent for r<=20.2.
