MADISON, Wis. -- Four athletic directors in the Madison Metropolitan School District are getting their jobs back if they want them, according to a ruling by an arbitrator on Monday.

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The arbitrator was working through a dispute between the school district and the teachers' union regarding the elimination of the athletic directors' positions.

This is the first year that the district has had two athletic directors instead of four at its high schools.

However, the arbitrator said that this arrangement broke the union contract. Last year, the school board voted to replace the four athletic director positions with two managerial athletic directors. The union officials subsequently filed a grievance.

The arbitrator said that that action violated the collective bargaining agreement with the union, Madison Teachers Inc. and has rule that all four should be re-instated with back pay and compensation for financial losses.

The arbitrator made the ruling last week but the union announced it on Monday, WISC-TV reported.

John Matthews, the union's executive director, said that he thought the ruling should foster improved communications between school officials and the union.

"I would think that this would mean to the incoming superintendent that we ought to really try to work these things through, and if we can't, we ought to appraise how we can bridge that gap," he said.

Boyce Hodge, the former Madison West High School athletic director, said that he's pleased with the arbitrator's decision. Hodge is still teaching at the high school.

"It's been a long 13, 14 months, and to have this decision rule in favor of the union today and the four athletic directors brought about a sense of huge relief for me personally," he said.

Hodge said that he recently involuntarily resigned from his position as basketball coach at the school. He said his participation in this arbitration led the district to force him to resign.

He said that he'll also challenge that decision and he hopes to return to the job as athletic director.

A school district spokesman said Monday they hadn't received the arbitrator's decision and declined to comment.

The fate of the district's two new managerial athletic directors is uncertain. Union officials said that they were signed to two year contracts with the district, WISC-TV reported.

Matthews said because of that as well as the costs of the back pay for the ousted athletic directors, this school board decision might cost $400,000.

Stay tuned to WISC-TV and Channel 3000 for continuing coverage.