An adult male of a newly discovered strepsipteran species from Brazil—Bahiaxenos relictus—is described. A new family Bahiaxenidae is suggested based on cladistic analyses of comprehensive morphological data sets with a broad taxon sampling including the stem group. It is unambiguously placed as the sister group of all other extant families of Strepsiptera. Bahiaxenos relictus is the only species of basal, i.e. non-stylopidian, Strepsiptera occurring in the New World. It appears to be a relict taxon that has survived in the fossil sand dunes of the São Francisco River (Bahia State). The loss of the 8th antennomere and the greatly reduced labrum are autapomorphies of Strepsiptera s.s. excluding Bahiaxenidae. The sister group relationship between†Protoxenidae and the remaining Strepsiptera, and between †Cretostylops and a clade comprising †Mengea and Strepsiptera s.s., is confirmed, as is the monophyly of Stylopidia and Stylopiformia.