The polishing method of the non-oxide single-crystal substrate

The non-oxide single crystal substrate of the silicon carbide single crystal substrate or the like, and polished at a high polishing rate, to provide a polishing method for obtaining a high-quality surface having excellent surface quality in smoothness. The polishing method, the polishing liquid is supplied to the polishing pad without containing abrasive grains, it is brought into contact with the polished surface of the non-oxide single crystal substrate and said polishing pad, a method of polishing by relative movement therebetween , the polishing liquid, oxidation-reduction potential of more than 0.5V, the oxidizing agent containing a transition metal, and a water, wherein the free of abrasive grains.