A new form of glass fiber is investigated. The core of the fiber is eccentrically positioned and contacts only a very small part of the inner surface of the outer tube with a lower index of refraction than that of the core. The total loss measured was 10 dB/km at a 0.80‐&mgr;m wavelength and the pulse broadening measured on a 55‐m section was 0.11 ns, which is much smaller than the value expected for the unclad fiber. Thus, it is shown that the part making contact between the core and tube dominates the transmission characteristics.