Parachordatortilis n. g. is proposed as a monotypic genus for Parachordatortilis mathevossianae (Petrov & Chertkova, 1950) n. comb. (Spirurida, Acuariidae), previously Dispharynx mathevossianae Petrov & Chertkova, 1950. The new genus can be distinguished from all other acuariid genera by having cordons with a sinistral torsion. Parachordatortilis possesses cordons consisting of two rows of delicate cuticular plates delimiting a longitudinal canal. This pattern of cordon structure suggests that Parachordatortilis is closely related to Dispharynx Railliet, Henry & Sisoff, 1912, Synhimantus Railliet, Henry & Sisoff, 1912 and Chordatortilis Machado de Mendonça & Olivera de Rodrigues, 1985. P. mathevossianae is redescribed on the basis of light and scanning electron microscopical observations of specimens collected from a common kestrel Falco tinnunculus L. in southern Italy.