A method for DNA sequencing has been developed that utilises libraries of cloned randomly-fragmented DNA. The DNA to be sequenced is first subjected to limit attach by a non-specific endonuclease (DNase I in the presence of Mn++), fractionated by size and cloned in a single-stranded phage vector. Clones are then picked at random and used to provide a template for sequencing by the dideoxynucleotide chain termination method. This technique was used to sequence completely a 4257 bp EcoRI fragment of bovine mitochondrial DNA. The cloned fragments were evenly distributed with respect to the EcoRI fragment, and completion of the entire sequence required the construction of only a single library. In general, once a clone library has been prepared, the speed of this approach (greater than 1000 nucleotides of randomly selected sequence per day) is limited mainly by the rate at which the data can be processed. Because the clones are selected randomly, however, the average amount of new sequence information per clone is substantially diminished as the sequence near completion.