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In this paper, we present some patterns related to derangements. We find the distribution of the \( \delta’ \)-transformation applied to all unicyclic derangements of order \( n \), and the distribution of the \( \delta’ \)-transformation applied to all derangements of order \( n \), considered in one-line notation. We introduce the notion of a matrix of forbidden pairs that helps us in solving our problems. We also give and prove a theorem related to derangements.