The Phaistos Disk is an ancient artifact from Crete. At each side of the disk, a series of unknown signs is written along a spiral. Professional archaeologists expect that we will only learn what it is until similar objects are found. A statistical analysis in this article shows what it is not: it is not a one-dimensional text, since there are relations between the signs in adjacent windings of the spiral. Three patterns of such relations have been identified. A Monte Carlo simulation of one of them has been performed, using a model of the spiral form. It is concluded that the probability of this pattern being coincidental is small, well below the conventional threshold.