In the Atlantic Ocean are three groups of islands that are politically part of Brazil and about which little seems to be known: the Fernando de Noronha Archipelago and the Rocks of Saint Peter and Saint Paul, both located near the equator and Trindade & Martim Vaz near the southern 20th parallel.
Interestingly, as many as four land bird species are known from these archipelagos, of which at least three are truly native and endemic: the Noronha Olive Tyrant (Elaenia ridleyana Sharpe) (Tyrannidae), the extinct Noronha Rail (cf. Rallus sp.) (Rallidae), the Noronha Vireo (Vireo gracilirostris Sharpe) (Vireonidae) and the Noronha Eared Dove (Zenaida auriculata ssp. noronha Sharpe) (Columbidae), all native to the largest archipelago, Fernando de Noronha.
There are also two more or less hypothetical forms for the second largest archipelago, Trindade & Martim Vaz: a pigeon form mentioned only by one of the first visitors to Trindade island at the end of the 17th century:
“In 1698 Dr. Halley visited the island, and says he found nothing living but doves and land-crabs.” 
And, for the time being, purely hypothetical but very probable, a rail, also for this one island.
No serious excavation appears to have taken place on any of the islands, such excavation would almost certainly unearth other bird forms that are now extinct.
 R. Davis: Real Soldiers of Fortune. Charles Scribner’s Sons, New York 1906
 Robert Cushman Murphy: The birdlife of Trinidad Islet. The Auk 32(3): 332-348. 1915
 S. L. Olson: Natural history of vertebrates on the Brazilian islands of the mid South Atlantic. National Geographic Society Research Reports 13: 481-492. 1981
 Ruy José Válka Alves; Nílber Gonçalves da Silva: Três Séculos de História Natural na Ilha da Trindade com Comentários Sobre Sua Conservação. Smashwords 2016