A Darwin school teacher has been stood down after allegedly posting a Facebook rant the day after a student killed himself, in which he described the teenager as a "bully" and a "disrespectful little brat".

The Northern Territory Department of Education said the teacher's alleged actions were disrespectful and would not be tolerated, after his message was widely circulated and heavily criticised on social media this week.

The Facebook post reads: “You were a bully to kids smaller and younger than yourself, I saw you intimidate, stand over and beat up on younger kids (never anyone your own size).

“You made life hell for genuine students wanting to learn and teachers trying to teach.

"You were a moody, disrespectful little brat in and away from school who was always given excuses by your parents and soft people in authority. Your [sic] gone, good no sympathy or empathy from me ...”