The Secondary Principals Association says the Ministry of Education should fine the company that developed the new school payroll system.
The Novopay system, developed by the Australian company, Talent2, has been beset by problems since its introduction more than two months ago.
Association secretary Patrick Walsh says if the ministry fined the company, it could use the money to compensate schools for the extra work caused by the problems.
The Novopay system has been responsible for about 8000 errors in teacher and support staff pay since it was introduced at the end of August this year. In some instances, staff were not paid at all.
The association says the mistakes are costing schools a lot of money in extra administrative work.
It says schools can't take legal action against Talent2 to get compensation, but the ministry can invoke the financial penalties in its contract with the company.
The ministry says penalties are possible, but has refused to say if they have been imposed.
The association says schools have a right to know if Talent2 has been fined.
Meanwhile, the Post Primary Teachers Association was to decide on Monday whether to invoice the Education Ministry for the errors.
Union president Robin Duff says that school administrators have spent hours fixing the problems and need to be reimbursed. He hopes charging for the hours involved will encourage the ministry to sort out the system.
Minister assured privacy breach a one-off
Associate Education Minister Craig Foss says he still has confidence in the new school payroll system, despite yet another mishap.
A data entry error meant Marshall Laing Primary School in Auckland was able to access confidential details of employees of another Auckland school, Northcote College.
Mr Foss says the primary school would have been able to change the employee details of Northcote College, but would not have been able to move money between bank accounts.
The minister says that particular problem has been rectified and he has been assured it was a one off. He retains confidence in the Novopay system, saying about 7000 problems have been fixed since its introduction.
"Yes I do have confidence in Novopay and that's driven by the fact that we've had about 450, 000 paid transactions since it began; there'll be another 90-odd thousand this week.
"But I fully acknowledge the frustration that many non-fulltime staff have had regarding the backlog of issues in their communications and the service centre."
Scrap the system, say principals
The Principals' Federation says the serious privacy breach caused by the Novopay system shows it is inherently flawed and should be scrapped.
President Paul Drummond says the latest problem following thousands of earlier payment errors is alarming, but not surprising.
"Clearly, the fact that it can happen is of considerable concern. I have some confidence, however, that schools wouldn't obviously make use of that particular error. But the fact that it can happen it is another signal that this Novopay system has inherent problems."
The federation says the problems are continuing unabated, with new errors that were not happening in the early weeks being reported.