Let P=P1,...,PM and Q=Q1,...,Qn be two patterns of points. Each pairing (Pi,Qj) of a point of P with a point of Q defines a relative dsiplacemtn delta ij of the two patterns. We can define a figure of merit for delta ij according to how closely other point pairs coincide under delta ij. If there exists a displacement delta 0 for which P and Q match reasonably well, the pairings for which delta ij approximately = delta 0 will have high merit scores, while other pairings will not. The scores can then be recomputed, giving weights to the other point pairs based on their own scores; and this process can be iterated. When this is done, the scores of pairs that correspond under delta 0 remain relatively high, while those of other pairs become low. Examples of this method of point pattern matching are given, and its possible advantages relative to other methods are discussed.