Glass sponges of the class Hexactinellida are a group of the most ancient multicellular animals, whose fossil remnants from the early Proterozoic have been registered. In order to demineralize the skeletal structures of the glass sponge Hyalonema sieboldi, we have used for the first time a strategy of slow leaching of the silicon-bearing component, based on the usage of alkaline solutions of sodium hydroxide, sodium dodecyl sulfate, and an anionic biosurfactant of a rhamnolipid nature. The obtained data unequivocally corroborate the presence of a fibrillar protein matrix functioning as a basis for silicon biomineralization in the basal spicules of H. sieboldi. Also, it has been found for the first time that the protein matrix is constructed of a collagenous protein. The technical approach proposed here might appear important for the study of the structural organization of skeletons in other silicon-bearing animals and, in an applied aspect, to work out new biomaterials for implantology and biocomposites, in order to use the latter as bioactive additives.