Self-stabilizing algorithms model distributed systems, which automatically recover from transient failures in the state of the system. The center of a graph comprises a set of vertices with minimum eccentricity. Farley and Proskurowski showed the linear time algorithm for locating the center of an outerplanar graph in the classical computing paradigm. The present paper investigates the selfstabilizing algorithm for finding the center of maximal outerplanar graphs, using a new approach with dual trees.