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The worker, who has since been laid off, is believed to have introduced the Metrion cascade 111 virus to the system while playing a computer game.
The Metrion virus, which infects executable files and overwrites batch and HTML files, affected 200 PCs. Network managers switched off the entire system to prevent its spread.
Aberdeen City Council suffered a virus attack in February that cost £10,000 to fix. Council IT chiefs said both incidents had been well handled.
The local Unison trade union branch questioned the level of staff training in IT and knowledge of the council's security policy.