The detection of high-redshift quasars (z > 3) offers the most direct method for studying conditions in the Universe at early epochs. Analysis of the changes in the luminosity function of the quasar population places constraints on the epoch of formation of massive, gravitationally bound systems, while detailed observations of the quasar spectra provide information on the properties and evolution of intervening absorption systems such as the Lyman-α clouds. We report here the discovery of two new quasars of very high redshift; Q0051 - 279 of z=4.43 and Q0101 - 304 of z=4.07. These two quasars bring to five the total number of quasars known with z>4 (refs 1-3). The redshift of Q0051 - 279 is the highest yet recorded and compares with the z =4.11 of the previous most distant known quasar3. Both new quasars were found by the same multicolour technique and in the same UK-Schmidt-Telescope (UKST) field as Q0046-293, the first quasar found with a redshift z>4 (ref. 1). The multicolour selection technique, coupled with other quantitative searches now in progress, provides the means for deriving a greatly improved description of quasar evolution at high redshifts.