The assignment of frequencies to radio transmitters in a mobile telecommunications network in such a way as to provide total coverage for a designated area is a problem of enormous interest to the telecommunications industry. This Frequency Assignment Problem has traditionally been modelled with binary constraints making it analogous to generalised graph colouring (A well known problem from discrete mathematics). In this paper we examine the use of non-binary high order constraints for the frequency assignment problem. The high order constraint representation allows small groups of interfering transmitters to be constrained by a single constraint that would have otherwise been constrained by a collection of binary constraints forming a clique. These higher order constraints are then solved by a high arity constraint solver. The results show that the application of high order constraints to the Frequency Assignment Problem introduces some flexibility at a local level that is not possib..