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This paper investigates a novel type of optical fiber which is composed of three portions: the core, inner cladding, and outer cladding. It is assumed that the core has the largest refractive index of the three, and the outer cladding index is the next largest. When the index difference between the core and the inner cladding is much larger than that between the outer cladding and the inner, the new fiber has a stronger confinement property than a usual singly clad fiber in the single-mode region. It is also assumed that the inner-cladding thickness is larger than or comparable with the core radius. This confinement is the origin of the following three properties of potential importance in single-mode optical communication. 1) As compared with a singly clad fiber, the largest core area for single-mode operation is roughly twice. 2) The group delay arising from waveguide characteristics has an opposite sign against that of typical glass dispersion. (Singly clad fiber has a dispersion of the same sign.) 3) The field is much more tightly confined within the core as compared with a singly clad fiber. This minimizes extra attenuation due to absorption in the cladding.