Facebook has taken serious note of the several instances of cyber bullying and is on the task of designing strict security measures to curb abuse.
Engineers at Facebook are reportedly working on new systems to fight the trend of "trolling", where anonymous online users "bombard" victims with offensive messages or abuse.
The news comes weeks after the announcement that children using Facebook could now report bullying and suspicious behaviour directly to the authorities after the launch of a new application.
The application called "ClickCEOP" had been downloaded more than 10,000 times since its launch last month.
"We're working with Facebook. They are a good partner and we're going to get closer and closer to them," The Telegraph quoted Jim Gamble, the chief executive of the Child Exploitation and Online Protection Centre (CEOP), as telling ITV News.
Gamble had warned the site that officers had seen a significant increase in complaints from parents and children reporting alleged paedophiles, bullies and hackers who were exploiting the site.
A Facebook spokesman said that engineers were developing new programmes to combat the threat.
"Users who send lots of messages to non-friends, for example, or whose friend requests are rejected at a high rate, are marked as suspect," he said.
He added, "Through the reporting process our team is also able to identify additional accounts using the same IP address so it is possible in certain situations to proactively remove multiple fake accounts."