Axial undulations in fishes are powered by a series of three–dimensionally folded myomeres separated by sheets of connective tissue, the myosepta. Myosepta have been hypothesized to function as transmitters of muscular forces to axial structures during swimming, but the difficulty of studying these delicate complex structures has precluded a more complete understanding of myoseptal mechanics. We have developed a new combination of techniques for visualizing the three–dimensional morphology of myosepta, and here we present their collagen–fibre architecture based on examination of 62 species representing all of the major clades of notochordates. In all gnathostome fishes, each myoseptum bears a set of six specifically arranged tendons. Because these tendons are not present outside the gnathostomes (i.e. they are absent from lampreys, hagfishes and lancelets), they represent evolutionary novelties of the gnathostome ancestor. This arrangement has remained unchanged throughout 400 Myr of gnathostome evolution, changing only on the transition to land. The high uniformity of myoseptal architecture in gnathostome fishes indicates functional significance and may be a key to understanding general principles of fish swimming mechanics. In the design of future experiments or biomechanical models, myosepta have to be regarded as tendons that can distribute forces in specific directions.