In the interest of producing high-strength splice connections between silica-based glass fibers a method of using a tri-particle flow of gases for flame fusion is disclosed. An outer relatively high-velocity flow of oxygen surrounds an intermediate, lower-velocity flow of chlorine or oxygen which in turn surrounds a central flow of H.sub.2, D.sub.2, NH.sub.3, or ND.sub.3.Particularly high strengths are achieved when a central flow of hydrogen or deuterium and an intermediate flow of chlorine are used in such a fashion as to heat fiber ends to be spliced to temperatures of 500 degrees C. and beyond only after these ends have been enveloped by chlorine.