The method provides CaF.sub.2 single crystals with low scattering, small refractive index differences and few small angle grain boundaries, which can be tempered at elevated temperatures. In the method a CaF.sub.2 starting material is heat-treated for at least five hours at temperatures between 1000.degree. C. and 1250.degree. C. and then sublimed at a sublimation temperature of at least 1100.degree. C. in a vacuum of at most 5*10.sub.-4 mbar to form a vapor. The vapor is condensed at a condensation temperature of at least 500.degree. C., which is at least 20.degree. C. below the sublimitation temperature, to form a condensate. Then a melt formed from the condensate is cooled in a controlled manner to obtain the single crystal, which is subsequently tempered. The method is preferably performed with a CaF.sub.2 starting material including waste material and cuttings from previously used melts.