The proposed inventions pertain to technology of continuous inorganic fibers manufacturing by way of drawing from melted minerals. Such continuous inorganic fibers may be used in production of heat-resistant threads, rovings, cut fibers, fabrics, composition materials and products based on such materials. The C contains the mixture of silicon (SiO2), aluminum (Al2O3), titan (TiO2), iron (Fe2O3 and FeO), calcium (CaO), magnesium (MgO), manganese (MnO) oxides and admixtures, and, according to the invention, this composition further contains potassium (K2O), sodium (Na2O), barium (BaO) oxides with the following components ratio (in mass %): Al2O315.90-18.10 TiO20.75-1.20 Fe2O3 + FeO7.51-9.53 CaO6.41-8.95 MgO2.50-6.40 K2O1.60-2.72 Na2O3.30-4.10 P2O50.23-0.50 SO30.02-0.15 MnO0.12-0.21 BaO0.05-0.19 admixtures,up to 1.00 SiO2the rest. The M comprises operations of the crushed composition loading into the melting furnace, melting, melt homogenization, subsequent stabilization of the melt in the melting furnace feeder, drawing, lubrication and winding the fiber onto the reel, and, according to the invention, the composition is held in alkaline solution during 15 to 20 minutes, then washed by running water during 20 to 30 minutes, dried and loaded into the melting furnace after such washing and drying. The feature of the proposed M is the use of sodium hydroxide (NaOH) and potassium hydroxide (KOH) solution in the range of about 0.1 to 0.5 N concentration as the alkaline solution. The inventions aim at providing the means for obtaining stronger and chemically more stable fibers by way of creating the conditions for decreasing the number of defects on the fiber surfaces.