The name conviva group is proposed for a group of five species of the genus Baeturia Stål, 1866, from the Moluccas and the Vogelkop peninsula (= Tjendrawasih), New Guinea. The monophyletic origin of this group is made plausible. Three of the species (B. conviva, B. quadrifida and B. schulzi) are redescribed, while two (B. laureli and B. hardyi) are described as new. For B. schulzi a lectotype is designated. B. hirsuta Blöte, 1960 is brought into the synonymy of B. quadrifida Walker, 1868. A key to the males and a map of the distributions are presented. Biogeographical data of this group suggest an Outer Melanesian Arc distribution.