We report the discovery of two radio-loud quasars with redshifts greater than 4: GB1428 + 4217, with z = 4.72, and GB1713 + 2148 with z = 4.01. This doubles the number of published radio-selected quasars with z>4, bringing the total to 4. GB1428 + 4217 is the third most distant quasar known and the highest redshift radio and X-ray source currently known. It has a radio flux density at 5 GHz of 259 +/- 31 mJy and an optical magnitude of R similar to 20.9. The rest frame absolute UV magnitude, M-v(1450 Angstrom), is -26.7, similar to that of the archetypal radio-selected quasar 3C273 [z = 0.158; M-v(1450 Angstrom) = -26.4]. GB1428 + 4217 is tentatively detected in ROSAT PSPC observations, which has been confirmed by more recent ROSAT observations described in a companion paper by Fabian et al. Both quasars were discovered during the CCD imaging phase of an investigation into the evolution of the space density of radio-loud quasars at high redshift. Combined with our earlier survey results, these objects give a lower limit on the space density of quasars with radio power P-5GHz > 5.8 x 10(26) W Hz(-1) sr(-1) between z = 4 and z = 5 of 1.4 +/- 0.9 x 10(-10) Mpc(-3). This can be compared to 2.9 +/- 0.2 x 10(-10) Mpc(-3) at z = 2 from Dunlop & Peacock for flat-spectrum sources of the same luminosity.