We describe a new technique for the parameterization of isosurfaces which result form the marching cubes (mc) algorithm. The motivation for the methods is based upon the method of chord length parameterization for curves. The method of extending the concept of curve parameterization to isosurface parameterization is based upon a relatively simple but very useful observation about a subset of the edge topology of a mc produced isosurface called the 4*-network. This is a collection of three mutually orthogonal planar polygons lying on and intersecting at the vertices of the isosurface. We illustrate the potential usefulness of this new parameterization method with examples from geometric modeling and medical imaging analysis.