Nearly three quarters (72 percent) of children claim they wouldn't participate in cyberbullying, says Symantec.
For some time there have been concerns that many children have been victims of bullying by other kids online.
However, the security vendor's Norton Online Family Report revealed that children's behaviour online is improving, as is their tendency to get help dealing with cyberbullying.
While, more than half (55 percent) admitted they had experienced negative online behaviour, over three quarters of kids said they would speak to their parents if they were threatened with physical harm or were sent suspicious or inappropriate material when online.
Furthermore, nearly two thirds (63 percent) said they would tell a teacher or a parent if they suspected a peer was being bullied.
Symantec also revealed that 63 percent of kids wouldn't do or say anything online that they wouldn't do offline, and 61 percent said harassing people online was unacceptable.
Kids are also well aware that file-sharing copyrighted content is also wrong, according to the report. Four in five admitted they knew that downloading a movie they haven't paid for is wrong, while 76 percent understood that downloading music without paying for it is also illegal.
"Firstly we should say well done to parents. This report shows that British parents have a good idea of most activities that their children undertake online," said Dr Katherine Rake, chief executive of the Family and Parenting Institute.
"You don't have to be a 'techie' to follow some basic tips for keeping your children safe on the internet. For example, family computers can be placed in a communal area so that children are supervised online. Keep talking to your children about cybercrime."
Rake added that internet safety isn't just down to families.
"There is a collective responsibility shared between parents, internet service providers, websites and regulators."
Marian Merritt, Norton internet safety advocate, added: "We believe that cybersafety and cybersecurity go hand in hand and children should learn about protecting themselves online the moment they first get connected".