Background information Edit
The Betelgeusians were designed by Fred Phillips and Robert Fletcher for The Motion Picture. With the approval of Gene Roddenberry, the Betelgeusians, as well as numerous other new species in the film, were named by Fletcher and provided a backstory by him. The following is a brief description, in Fletcher's own words:
"BETELGEUSIANS – Name taken from the real star. All tall, seven feet and over. Humanoid with characteristics combining eagle and leopard. Derived in evolution from giant leopardlike birds, have claw and bone structure like condor but walk upright like leopards. Costumes: materials found stored in Paramount for as long as forty years. Jewelry made of fabric, but electro-plated." (The Making of Star Trek: The Motion Picture, p. 130)
In an interview with Robert Fletcher – published as part one of "The Star Trek Costumes", in the February 1980 edition of Fantastic Films – the Betelgeusians were described thus; "Although humanoid in conformation, they are evolutionary derivitives of a race of creatures combining characteristics of eagles and leopards." 
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 Betelgeusians, as taken from Fletcher's original background notes, added:
"The inhabitants of the real star Betelgeuse were seven-foot-tall humanoids who were actually descended from a race of leopard-like eagles. They had claw and bone-like structures like a condor, but walked upright."
The robe worn by the Betelgeusian ambassador was one of several costumes made from bolts of rare fabric, scavenged from storerooms around the Paramount lot, for the San Francisco crowd scenes. This particular fabric was originally hand-picked by Cecil B. DeMille for a 1939 production, and was made of silk thread with real gold and silver details. The estimated cost for the costume was at least US$10,000, probably making it the most expensive worn by an extra. (The Making of Star Trek: The Motion Picture, p. 129) The robe was auctioned as part of 2006's Profiles in History auction with an estimated sale price of US$1,000 to US$1,500; the final sale price was exactly US$1,000. 
Two additional Betelgeusian-related lots were included in the It's A Wrap! sale and auction, each containing an original Betelgeusian mask. The first lot sold for US$202.50.  The second – which contained three masks, original jewelry, and a bronze-colored robe – sold for US$732. 
According to the Star Trek: The Next Generation - Player's Guide, Betelgeusans come from the planet Betelgeuse IV, which they call "Hav'a'halar". Betelgeusans do not make any distinction between history and mythology. Every Betelgeusan chooses one of six heroes from their mythology to emulate. Betelgeusan society is divided into social groups that emulate the same hero.