Coals of bituminous to anthracite rank exhibit optically anisotropic character and behave as uniaxial negative or a biaxial substances. Consequently, maximum reflectance (Rmax) and minimum reflectance (Rmin) are measured under polarized light in rotating the microscope stage. The difference between Rmax and Rmin is called the optical anisotropy (reflectance anisotropy) or bireflectance. The relationship between vitrinite reflectance, the mostly used microscopic rank measure, and reflectance anisotropy determined by a method which has been newly proposed by the author is investigated. The following simple and multiple regression equations were obtained by a least squares method. When the value of the mean maximum reflectance (Romax) is 3.08% or less