The purpose of this note is to sharpen the results in Bouyssou and Pirlot (2005) giving an axiomatic characterization of concordance relations. We show how the conditions used in that paper can be weakened so as to become independent from the conditions needed to characterize a general conjoint measurement model tolerating intransitive and/or incomplete relations. This leads to a clearer characterization of concordance relations within this general model. Key words: Multiple criteria analysis, Concordance, Outranking methods, Conjoint measurement, Nontransitive preferences