(covers information from several alternate timelines)
Background information Edit
In an interview with Robert Fletcher – published in the February 1980 edition of Fantastic Films, as part one of a two-part interview with him, called "The Star Trek Costumes" – the name of this species was misspelled "K'norian" and they were described thus;
"Similar to Earthlings in all aspects save one: encased in a type of structural shell formation on top of the forehead is an additional brain structure enabling them to communicate over very long distances. Included in this brain structure is, in essence, an eighth sense, giving them the ability to deal with time and space dimensions – an ability we Earthlings sadly lack." 
In an article appearing in the January 2002 edition of Star Trek: The Magazine Volume 2, Issue 9, entitled "Who is that Alien?", the following information about the K'normians, as taken from Fletcher's original background notes, added:
"The K'normians were a mostly normal humanoid race, though they did have large foreheads not unlike the Klingons, which Fred Phillips also redesigned for The Motion Picture. The K'normians' large brains provided an eighth sense that gave them a superior appreciation of time and space."
According to Star Trek: Star Charts ("United Federation of Planets I" and "III"), K'normia (Psi Tauri) was the name of a star in the Alpha Quadrant. The primary was a Class F star. Magnitude of this star was +5, which was the same brightness as Sol. K'normia was the name of a planet in the system, too, and had, by 2378, become a member of the Federation.