We investigate the metallicity of the broad line region (BLR) of a sample of 30 quasars in the redshift range 4 < z < 6.4, by using near-IR and optical spectra. We focus on the ratio of the broad lines (SiIV1397+OIV]1402)/CIV1549, which is a good metallicity tracer of the BLR. We find that the metallicity of the BLR is very high even in QSOs at z∼6. The inferred metallicity of the BLR gas is so high (several times solar) that metal ejection or mixing with lower metallicity gas in the host galaxy is required to match the metallicities observed in local massive galaxies. On average, the observed metallicity changes neither among quasars in the observed redshift range 4 < z < 6.4, nor when compared with quasars at lower redshifts. We show that the apparent lack of metallicity evolution is a likely consequence of both the black hole-galaxy co-evolution and of selection effects. The data also suggest a lack of evolution in the carbon abundance, even among z > 6 quasars. The latter result is puzzling, since the minimum enrichment timescale of carbón is about 1 Gyr, i.e. longer than the age of the universe at z∼6.