And according to their victims, they can be selfish, insensitive and domineering people who will almost certainly feel insecure about themselves.
This profile of the bullying boss has emerged from research by Surrey University's psychology department for the Professional Association of Teachers.
PAT members are increasingly worried about bullying and, like the other teacher unions, PAT has seen a sharp rise in cases.
John Andrews, general secretary, said: "Bullying takes an enormous toll on teachers and therefore on pupils and education as a whole.
"The training of heads, deputy heads and other managers to manage people better and encourage communication with their colleagues should be a priority, as should training staff in assertiveness and confidence skills."
Almost a fifth of PAT members who responded to a survey by Surrey University complained they had been or were being bullied.
Many reported physical ailments and psychological consequences ranging from loss of self-esteem and confidence to anxiety and depression. One-third had visited their GP and half had to take time off work. Some even lost their job.
Robert Edelmann and Laura Thyeson from Surrey said there was a clear feeling that bullying was increasing, mainly due to pressures on heads and senior management to produce results amid financial constraints.
In their report, "Bullying at Work", they added: "The very people whom many staff no doubt look to for support, encouragement and firm but fair leadership are resorting to verbal threats, shouting and anger, undermining work or viewing such efforts negatively.
"The demands upon headteachers have increased and yet they receive little by way of training for their demanding managerial roles. It is perhaps inevitable that some may feel insecure in their position and, in the absence of appropriate skills, resort to bullying."
The findings are based on a survey of 1,000 people ranging from primary teachers to college lecturers. One primary teacher claimed to have been screamed at in front of pupils while a deputy head was told that her promotion was at risk if she did not accept a change of duties.
"The bullying consisted of almost constant nasty remarks designed to destroy my confidence," said one young teacher. A 58-year-old in a grant-maintained school added: "My work and efforts are deliberately rubbished by the new head."
The victims most often reacted by feeling upset, sad, surprised or shocked. Less frequently, they became angry, stood up for themselves or ignored the bullying. More than half of those who had been bullied said that over time they learnt to defend themselves.
Some teachers who had been bullied blamed it on the lack of training for heads and managers. "Bullying often seems to occur when someone is unsure in their own position and needs the feeling of imposing their seniority," said one respondent.