Unsworth, 33, scored the winning goal against Sheffield United to keep Wigan in the Barclays Premier League last season, but he was released by the Latics in the summer and joins the Clarets on a free transfer.
Clarets boss Steve Cotterill said after Saturday´s 2-1 win against West Bromwich: "He´s obviously going to be short of fitness and as you get older, it gets harder. But he will bring great experience to the dressing room."
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