The p-dispersion problem consists in locating p facilities at some n predefined locations, such that the minimum distance between two facilities is as large as possible. We propose in this paper an algorithm based on a combination of two approaches: the determination of cliques in a graph and the solution of mixed integer linear programs. Computational results are reported which prove the efficiency of the method. For example, randomly generated instances with up to 150 facilities can be solved for all values of p in a few minutes of CPU time.