A theoretical approach for linkage mapping the genome of any higher eukaryote is described. It uses the polymerase chain reaction, oligonucleotides of random sequence and single haploid cells. Markers are defined and then the DNA of a single sperm is broken at random (eg by gamma-rays) and physically split into 3 aliquots. Each aliquot is screened for the presence of each marker. Closely-linked markers are more likely to be found in the same aliquot than unlinked markers. The entire process is repeated with further sperm and the frequency that any two markers co-segregate determined. Closely-linked markers co-segregate from most cells; unlinked markers do so rarely. A map can then be constructed from these co-segregation frequencies. A specific application for determining the order and distance between sets of closely-linked and previously-defined markers is also described.