To my knowledge, all, not "some", unidirectional tires stay on the same side of the truck...the tread design works in the direction of rotation (arrows on the sidewall indicate the direction). My new set of Blizzak's are an example.Keep in mind not all tires are meant to be rotated in this order. Some unidirectional tires are not supposed to be cross-rotated (if it was originally on the right side, keep it on the right just switch it between front and rear wheels)
Steve