Well, since no one has commented yet with any knowledge about it ... I'll list some links.

In these links it says that the
"transcendent function is the union between the conscious and unconscious"
[spoil:9b6c2865c6]http://web.ukonline.co.uk/phil.williams/transcendent-function.htm
http://www.online.pacifica.edu/pgl/stories/storyReader$520[/spoil:9b6c2865c6]

In the following link it says:

"Transcendent function. A psychic function that arises from the tension between consciousness and the unconscious and supports their union. (See also opposites and tertium non datur.)"
[spoil:9b6c2865c6]http://www.compilerpress.atfreeweb.com/1.%20Jungian%20Lexicon.htm[/spoil:9b6c2865c6]


This one link gives a more varying definition:
Once a complex has been individuated, the transcendent function works to integrate that complex into a single unified Self, which, when it develops, encompasses and replaces all other complexes, becoming the whole of personality.
[spoil:9b6c2865c6]http://intropsych.mcmaster.ca/psych2b3/lectures/jung-2.html[/spoil:9b6c2865c6]


Something written on the cover of a book concerning the "Transcendent Function"
The transcendent function is the core of Carl Jung's theory of psychological growth and the heart of what he called individuation, the process by which one is guided in a teleological way toward the person one is meant to be. This book thoroughly reviews the transcendent function, analyzing both the 1958 version of the seminal essay that bears its name and the original version written in 1916. It also provides a word-by-word comparison of the two, along with every reference Jung made to the transcendent function in his written works, his letters, and his public seminars.
[spoil:9b6c2865c6]http://www.amazon.com/Transcendent-Function-Psychological-Dialogue-Unconscious/dp/0791459780[/spoil:9b6c2865c6]

It says in this link that the transcendent function is indeed a function of the psyche:

Jung here defines the transcendent function as not only an analytical method but also a natural function of the psyche (Dehing, 1993, p.222). Thus, the transcendent function is not only the thinking that a subject applies to matter, but also an inborn structure of the psyche, the mind (Inwood, 1992, p.79).
[spoil:9b6c2865c6]http://www.improverse.com/ed-articles/matthew_clapp_1997_feb_jung_column.htm[/spoil:9b6c2865c6]

This link says:

Nearly everyone who is familiar with Jungian psychology is aware that Jung had a deep interest in symbols and a symbolic understanding of events and images. When students of Jungian psychology first hear of the "transcendent function," however, many are surprised to learn that Jung equated it with "symbol." It is well that he did so; a true symbol is indeed transcendent and "function" suggests its active nature. The symbol transforms by bringing opposites together and transcending them. As Jung put it, the transcendent function is "the transition from one condition to another" (Let-I, p. 268). When this Congress theme was adopted, it elicited a remarkable variety of papers devoted to broadening and deepening our understanding of the transcendent function.
[spoil:9b6c2865c6]http://www.daimon.ch/3856305378_2P.htm[/spoil:9b6c2865c6]


Now, I know for a fact that the transcendent function is technically the midpoint between all of the other functions, but I can not find the quote where it says this although I know it is in one of Jungs books. I remember specifically reading and seeing a chart that shows the transcent function with the other functions. I will show you pretty much what the chart looked like: