C# - Best way to randomize two identical arrays without overlap?

Suppose we have two identical arrays {"A", "B", "C", "D", "E", "F"}. Is there a quick way to randomize the order of each that ensures when the two are lined up, the same letters are never at the same indices? (Obviously we can just generate a new index if it will cause a match but I'm wondering if there's a way that produces less repetition).