I. Introduction . The discrete ordinate method for radiative transfer is commonly ascribed to Chandrasekhar. [1] Computer implementations of that method were, however, plagued by numerical difficulties [2] to such an extent that researchers made little use of it. The purpose of this paper is to alert the community to a new numerical implementation of the discrete ordinate method for vertically inhomogeneous layered media which is free of these difficulties and to give a summary of its e...