"How can I get people to see what they're missing?" she said to herself. "I know: I'll get my old school to come down and put on a concert."
Two weeks later, three coaches arrived and 150 young musicians and singers really socked it to Margaret's new friends in a demonstration of what a good music department could really do.
Margaret spoke at the end.
"I'm so grateful and proud," she said. "I wanted my staff and children and parents to see what was possible."
It took Jack, her senior deputy, to bring her back down to earth the following day.
"Margaret, everyone's telling me I should have spoken up earlier," he said.
"But as our new head you had to have the benefit of the doubt. Surely, though, with your experience you've learnt that the one thing you don't do is go into a new school and keep going on about what happened at your old place?"
Margaret was mortified. She knew what Jack meant, but somehow she hadn't seen her concert like that.
"I just thought I could kick-start things a bit," she said. "I knew we'd have a good concert. The music at my last school was admired everywhere."
Jack replied: "But that means little to us, don't you see? It patronised us, and it seemed to say that part of you is still back there with them.
And how do you think other departments feel, with all of them crying out for your attention?"
Margaret nodded. "What now?" she asked.
"Nobody will mind your starting with music," said Jack. "We all know it needs the kiss of life. But Steve, the head of department, really has it in him. But he needs support, cash and encouragement much more than he needs to be told how good other schools are.
"Maybe we'll end up with a rock group, or a steel band, or a skiffle group - lord knows! But it'll all be ours, and we'll be proud of it. OK?"
"OK, Jack," the head conceded.
"Then," said Jack, "will you try to work your way through each department in the same way? You really can do this, and that's why you got the job.
And we're all on your side."
Some names and personal details have been changed