The damage was caused when Celtic clinched the title
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Celtic are to pay Kilmarnock £20,000 for damage caused to seats during the Rugby Park fixture when Gordon Strachan's side clinched the SPL title.
About 1,500 seats were broken in the Chadwick and Moffat stands as Celtic fans celebrated their side winning the Championship on 9 April.
Celtic also paid for damage caused by some fans at Rugby Park in 2004.
The SPL then introduced rules to ensure clubs responsible for damage at away grounds paid for the repairs.
The contractors aim to have Rugby Park fully repaired for their final SPL home match of the season against Hearts.