The native writing system is called pIqaD but the canonical works say nothing about it. There have been many artist representations of it over the years, but few have been usable in any practical sense.
Early in the Klingon Language Institute's existence it received information, through another organization which claimed to have received information from someone at Paramount Pictures, about a collection of symbols that had been mapped to the 26 letters/sounds of the language. This was the first usable pIqaD system released for the language. The symbols are shown below with buttons that play an audio explanation of the sound:
a | b | c | d | e | g | h |
i | j | l | m | n | f | o |
p | k | q | r | s | t | x |
u | v | w | y | z | ||
1 | 2 | 3 | 4 | 5 | 6 | 7 |
8 | 9 | 0 |
The organization that originally published these symbols claimed that specific artists that worked on Star Trek provided the symbols to them. However, after reaching out to those artists, none claimed ownership of it. The author of this site believes that it is possible that someone at the other organization actually created them and the claim that they came from a leaked source was fabricated to add credence to them.
Since none of the Star Trek artists have claimed ownership of them, and Paramount/CBS has not claimed ownership of them, the author of this site believes that this pIqaD system not owned by them.