Certain proteins, of which collagen is the best known example, have an approximately periodic sequence of amino acids. Evidence is available that the nucleic acid templates of at least some of these proteins have a large amount of internal self-complementarity. It is difficult to explain the origin of such proteins from nonperiodic proteins by accumulation of single amino acid replacements. A saltatory origin is suggested; the process would be a repetitive replication of a small nucleic acid segment. Internal self-complementarity occurs because the repeating segment incorporates sequences from both strands of DNA. The same process could produce RNA with a large amount of internal self-complementarity; tRNA may be an example.