We examined dinucleotide relative abundances and their biases in recent sequences of eukaryotic genomes and chromosomes, including human chromosomes 21 and 22, Saccharomyces cerevisiae, Arabidopsis thaliana, and Drosophila melanogaster. We found that dinucleotide relative abundances are remarkably constant across human chromosomes and within the DNA of a particular species. The dinucleotide biases differ between species, providing a genome signature that is characteristic of the bulk properties of an organism's DNA. We detail the relations between species genome signatures and suggest possible mechanisms for their origin and maintenance.