He said in the post that fighting and threatening others, regardless of how it started, was unacceptable in the school and it was investigating two incidents of this.
"Some students have already been stood down for this and it is likely that a small number of students may be suspended.
"We have started identifying some of the 'confession page' ringleaders and getting help from technicians to collect the information we need to refer this to the police and/or suspend/discipline these students – who are not only breaking the law and their friends' trust but also our school's values."
McMillan was approached for comment about the alleged bullying on Wednesday and today but is yet to respond.
Netsafe spokesman Sean Lyons said parents should look for key signs of online bullying such as withdrawing from social activities or platforms that they may have previously frequented and they may suddenly start speaking about a new group of friends.
"Often the parents when they worry about these things, the parents' first move might be to say, I want to see, you know give me your phone, show me your phone, show me what's been going on. Let me read those messages."
To parents, he said some messages seem benign when they are actually harmful, or look "really awful" but to the young person it's just "banter".
Lyons said it's important parents talk to young people and work alongside each other to find a solution.
"We know from our research that one of the most worrying parts of young peoples' response to serious online incidents is a chunk of young people that do nothing. And for us, that's the real danger."
By speaking to young people about their options, he said they'll realise there are actions that can be taken, such as contacting the platform or making a complaint under the harmful digital communications act.
McMillan wrote that, sadly, bullying happens in all sorts of places, including adult workplaces and his school.
He asked parents to speak to their child about the situation and ask to check their phone to make sure they aren't being bullied or caught up in the bullying of others.
"If your child is being bullied please let us know and also encourage them to let their favourite teacher, their tutor teacher, a youth worker, dean, counsellor or a student leader know."