An improvement is proposed, in a method for the preparation of a step-index silica glass preform as a precursor of optical fibers by completing the cladding layer of the secondary preform by the outer deposition on and around a primary preform consisting of the center core and side core, to conduct the outer deposition for the cladding layer in such a way that the inequality .vertline.d.lambda..sub.0 /dk.vertline..ltoreq.500 nm is satisfied, in which k is the ratio of the diameter of the primary preform to the diameter of the secondary preform and .lambda..sub.0 is the zero-dispersion wavelength in nm of an optical fiber obtained by drawing the secondary preform, d.lambda..sub.0 /dk being the differential of a function held between .lambda..sub.0 and k determined beforehand from the distribution of the refractive index within the primary preform. When the outer deposition is performed in this way, a great improvement can be obtained in the uniformity of the zero-dispersion wavelength of the optical fiber prepared by drawing the preform.