When a linearly polarized light is launched into a birefringent material, the output light is generally elliptically polarized. The ratio of the major and minor axes of the polarization ellipse varies depending on the angle between the polarization direction of the input light and the birefringent axis of the medium. The maximum ratio is determined only by the retardation due to the birefringence. Utilizing this phenomena, birefringence of a medium whose principal axis direction is unclear is measured with high precision by measuring the maximum extinction ratio for various input light polarization directions. Ambiguity in retardation associated with angular function solution is removed by measurement at two adjacent wavelengths. The measurement principle of the new method is confirmed by applying it to a quarter wave plate made of quartz. Birefringence of a 3 m long ribbon fiber as small as 10-7 is successfully measured.