A magnet is a pair u,v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new vertex linked to all common neighbours of u and v without changing the stability number. We characterize a class of graphs such that by repeated use of magnets the graph is reduced to a stable set. A description in terms of forbidden subgraphs is given and a polynomial algorithm follows.