Following the recent trend of studying the theory of belief revision under the Horn fragment of propo- sitional logic this paper develops a fully charac- terised Horn contraction which is analogous to the traditional transitively relational partial meet contraction [Alchourron et al., 1985]. This Horn con- traction extends the partial meet Horn contraction studied in [Delgrande and Wassermann, 2010] so that it is guided by a transitive relation that models the ordering of plausibility over sets of beliefs.