Mr Hyndman said staff and students were again evacuated immediately and police called.
Police arrived but there was a much reduced presence, and they did a walk through of the school and once again found no bomb, he said.
Mr Hyndman said after 35 minutes the all-clear was given.
"It is quite frustrating and highly inconvenient for everyone, but you have to treat these threats seriously," he said.
Brookfield School was one of six schools to have received bomb threats on Wednesday, and were are among 27 schools around the country who received similar threats yesterday.
Police say they are undertaking a number of lines of inquiry to establish the exact origin of these calls, and initial enquiries indicate the calls originated from overseas.