This paper introduces a non-H rule WRM which is a weak form of rational monotony. We explore the effects of adding this non-H rule to the rules for the preferential inference. In this paper, a relation ｜～ is said to be P ＋ WRM iff it is a preferential inference and satisfies the rule WRM. We establish the representation theorem for P＋WRM, and compare the strength of WRM with some non-H rules appearing in literatures. Moreover, we explore the relation between P＋WRM and conditional logic, and demonstrate that P＋WRM is equivalent to ‘flat’ fragment of conditional logic CS4.2. Another contribution of this paper is to explore the relation between two special kinds of preferential models, i.e., PRC model and quasi-linear model. Main result reveals that the latter is a special form of the former.