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Fibrous silicon dioxide material that is resistant to high temperatures, particularly in the form of mats or plates, is produced by dry-spinning water glass into water glass fibers, the water glass fibers being then transformed into silica fibers by treatment with aqueous acid or salt solutions that contain hydrogen ions. The silica fibers are thereupon treated with an agent that accelerates the formation of cristobalite from amorphous silica. Such agents include, in particular, alkali hydrogen phosphates, sodium acetate and solium chloride. The fibers are dried and dehydrated at temperatures above 600 DEG C., particularly between 950 DEG C. and 1050 DEG C., before or after treatment with the accelerating agent. There dehydration occurs after such treatment, the fibers are subsequently subjected to thermal aftertreatment. When subjected to 1500 DEG C. temperatures, the material thus obtained generally shrinks by less than 3%; it has very little tendency to become brittle and is particularly well suited for the fabrication of high temperature insulation material.