We revise the type material of the enigmatic fossil insect Carbotriplura kukalovae Kluge, 1996 from the Pennsylvanian of the Czech Republic. Multiple errors in the original description are documented and corrected. C. kukalovae is regarded as a possible transitional fossil link between Zygentoma and Pterygota. Carbotriplurida is therefore elevated to ordinal rank and considered as putative fossil sister group of Pterygota. The paranotal theory of the origin of insect wings and the parachute theory of origin of insect flight are briefly discussed and further corroborated. Testajapyx thomasi from the Pennsylvanian of Mazon Creek is tentatively considered as Dermaptera rather than Diplura.