The invention relates to semiconductor silicon technology. The inventive method consists in electolytically decomposing a silicon tetrafluoride-saturated eutectic melt of a ternary system of alkali metal fluoride salts. For saturating the melt, a silicon tetrafluoride obtainable by fluorinating a silicon dioxide is used, wherein said fluorination is carried out in two stages, i.e. at a first stage, an elemental fluorine is supplied with excess and a silicon dioxide is supplied at the second stage. The silicon powder separation from the fluoride salt eutectic melt is carried out by dissolving the silicon particles-containing melt with the aid of anhydrous hydrogen fluoride and by subsequently filtering for isolating a solid phase in the form of a silicon powder.