Background and aims – Euodia frauenfeldii has the characteristic ‘semi-circular’ or ‘crescent-shaped’ valves found in most species of Euodia, but as it also has a pair of conspicuous transapical costae, it was later transferred to Eunotogramma. Examination of the structure of its valves and girdle has led to a reassessment of its taxonomic position. Material and methods – We discuss various aspects of terminology used for the parts of the valve, their abbreviations used throughout the literature and provide a detailed taxonomic background to both Euodia and Eunotogramma. Key results – A new genus, Moralesonia is described and its relationships discussed.