craniate

The skull is the bony structure in the head of a craniate.

The only vertebrate which does that is the Hagfish, which is a craniate, but is not universally accepted to be a vertebrate.

That is, the earliest craniate had a single median inhalant duct conveying water over the unpaired nasal sac on its way to the pharynx and gills.

Haikouichthys had a defined skull and other characteristics that have led paleontologists to label it a true craniate, and even to be popularly characterized as one of the earliest fishes.

Cladistic analysis indicates that the animal is probably a basal chordate or a basal craniate; but it does not possess sufficient features to be included uncontroversially even in either stem group.

The term "fish" most precisely describes any non-tetrapod craniate (i.e. an animal with a skull and in most cases a backbone) that has gills throughout life and whose limbs, if any, are in the shape of fins.