A tapered fiber bundle is formed by first etching the end portions of each fiber within the group so as to remove a selected amount of outer cladding material from each fiber. The assembled, etched fibers are then fused together in conventional fashion to form a fiber bundle. By first etching the fibers to form a "tapered" structure, the core diameter of the tapered fiber bundle remains intact; in the prior art, the tapering process of drawing down the fused collection of fibers would reduce the core diameter. Preferably, the outer cladding of the central single mode fiber is modified to exhibit the same etch rate as the outer cladding layer of the remaining fibers.