A new genus and species of tetraphyllidean cestode, Caulopatera pagei n. g., n. sp., is described from the grey carpetshark Chiloscyllium punctatum Müller & Henle in Moreton Bay, Australia. The new genus is placed in the Phyllobothriidae, subfamily Phyllobothriinae. Caulopatera n. g. is distinct from all other phyllobothriine genera in having stalked, circular, non-loculate bothridia that lack an apical sucker, testes that are restricted to the region anterior to the cirrus-sac and circum-medullary vitelline follicles. The new genus most closely resembles Carpobothrium Shipley & Hornell, 1906, with which it shares non-loculate, stalked, unhooked bothridia without an accessory sucker and testes that are entirely anterior to the cirrus-sac, but differs from it in that it lacks a slit-like opening in each bothridium and flaps surrounding the opening. The possession of bothridial stalks is consistent with two cestode orders, the Tetraphyllidea and the Rhinebothriidea. The morphology of the bothridial stalks is consistent with other tetraphyllidean genera, in that Caulopatera possesses triangular bothridial stalks surrounding the back of the bothridia, indicating that it belongs in the Tetraphyllidea senso stricto, rather than in the recently recognised Rhinebothriidea.