The graph partitioning problem consists of dividing a graph into parts or partitions which satisfy some specifications. This problem has several applications such image segmentation, load balancing and communities’ detection. Unfortunately, graph partitioning is known to be NP-complete. In this paper, we present, the first self-stabilizing algorithm for maximal partitioning arbitrary graph into triangles (SPT), then we present the correctness and convergence proofs of the proposed algorithm.