It was discovered in a wooded area at Byreburn, near Canonbie, a few miles from Gretna. The man, aged between 40 and 60, is thought to have lain in the wood for some time.
His body was found by two men out shooting game on the farmland.
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Hide AdA police spokesman said the man was bald, clean-shaven and fully dressed, wearing a brown jacket, a hat and gloves.