One of the problems in computer vision is to give a computer a representation of a scene and recognize the objects in the scene and their spatial relationships. This involves low-level vision (image processing), mid-level vision (feature extraction and measurement) and high-level vision (interpretation). One important part of high-level vision is relational matching, the process of matching two relational descriptions of objects, often for the purpose of object identification. This paper presents an improvement of the original method by Shapiro and Haralick for solving the relational distance graph matching problem for unlabeled graphs on a parallel computer.