Multiple Complete Digest (MCD) mapping is a method of determining the locations of restriction sites along a target DNA molecule. The resulting restriction map has many potential applications in DNA sequencing and genetics. In this work, we present a heuristic algorithm for fragment identification, a key step in the process of constructing an MCD map. Given measurements of the restriction fragment sizes from one or more complete digestions of each clone in a clone library covering the molecule to be mapped, the algorithm identifies groups of restriction fragments on different clones that correspond to the same region of the target DNA. Once these groups are correctly determined the desired map can be constructed by solving a system of simple linear inequalities. We demonstrate the effectiveness of our algorithm on real data provided by the Genome Center at the University of Washington.