Lissopedia, a new genus is proposed for Tetrapedia globulosa Friese, 1899, from Brazil and to include Tetrapedia flavopicta Cockerell, described from Yucatan, México. Three new species: Lissopedia ochronota from Albany, Jamaica, Lissopedia xanthina from Carmen (on the River Madre de Dios), Pando, Bolívia, and Lissopedia tristriata from Manaus, Amazonas, Brazil are described. The female of Lissopedia globulosa is described from Barreiras, Bahia, Brazil and thus a locality is given for this species. This genus seems to be confined to the Neotropical Region. Exomalopsini, Tapinotaspidini and Paratetrapediini are considered as tribes of Exomalopsinae.