A giant Ptyradactyl monster, much like Anguirus, only shows but in a few movies throughout the whole entire franchise. Like with Mothra, Rodan starred in his own movie, "Rodan" in 1956. Later appearing in "Godzilla: Final Wars" is seen attacking New York City.
Other appearances by this monster include:
Ghidrah, the Three-Headed Monster
Godzilla vs. Monster Zero (Or just referred to as "Monster Zero")
Destroy All Monsters
Godzilla vs. MechaGodzilla II
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Rodan art video - [link]