Over sufficiently long windows, complementary strands of DNA tend to have the same base composition. A few reports have indicated that this first-order parity rule extends at higher orders to oligonucleotide composition, at least in some organisms or taxa. However, the scientific literature falls short of providing a comprehensive study of reverse-complement symmetry at multiple orders and across the kingdom of life. It also lacks a characterization of this symmetry and a convincing explanation or clarification of its origin.