The female imago specimen belonging to a new species Baba lapidea gen. and sp. nov. and a new family Babidae fam. nov. from Eocene Baltic amber is described and illustrated. This insects combines characters common with Fimbriatotergaliae (on fore wing MP₂ and CuA curved near base; on hind wing MA lacks triad; first tarsal segment shortened and fused with tibia) with a plesiomorphy never found in Fimbriatotergaliae (mesonotal suture transverse). Possibly, Baba gen. nov. represents a sister taxon of Fimbriatotergaliae Kluge, 2004.