The cleavage of DNA by restriction endonucleases can be limited by the addition of ethidium bromide. When closed circular DNA is used as a substrate, DNA with one-site cleavages of one or both strands can be made by adding appropriate amounts of dye. The singly cleaved DNA is a complete set of full-length permuted linear molecules. Fractionation of the products of a digestion of the permuted linears with a single-hitting restriction endonuclease by gel electrophoresis yields a series of bands that can be used to determine relative molecular weights of the DNA fragments in the gel without the introduction of standards. It is possible to determine the relative molecular weight of a fragment to within +/-2.5%. These molecular weights immediately allow the determination of the HindIII and Hpa I maps of simian virus 40. The HindIII map of bacteriophage PM2 was determined by this method with one ambiguity that was resolved by using traditional techniques.