A new, well-preserved specimen of Palaeobates polaris from the Smithian 'fish horizon' of Spitsbergen (Svalbard archipelago, Arctic Norway) is presented. The find is more complete than the type material of P. polaris and contains amongst others the left mandibular branch with associated dentition and labial cartilage as well as elements of the hyoid arch and a portion of the anterior dorsal fin. P. polaris shares with the other species of the genus Palaeobates the same tooth histology (orthodont teeth with pulp cavity), but the ornamentation of the teeth is different. Several studies have shown that it is problematic to deduce phylogenetic relationships among hybodontiform sharks by means of tooth histology. Moreover, orthodont teeth with a pulp cavity are probably plesiomorphic for hybodontiforms. Based on the new find of P. polaris, three other characters are proposed to be apomorphic for Palaeobates in general: (1) the lower margin of the dental groove of Meckel's cartilage runs nearer to the ventral than to the dorsal border of the mandible in P. polaris but medially to these margins of the lower jaw in the crown group hybodontoid Acrodus; (2) the number of tooth files and arrangement of the teeth of P. polaris are well-distinguishable from those of Acrodus and Asteracanthus; and (3) the dorsal fin spines of P. polaris, and also of P. angustissimus, tend to be more slender compared to those of Hybodus and Acrodus. Nonetheless, more material is needed to ascertain if these traits are useful to separate Palaeobates from other hybodontiforms.