Negotiation is a form of interaction in which agents with conflicting preferences try to reach an agreement on an issue by exchanging offers. Since early nineties, the benefits of exchanging arguments, in addition to offers, has been advo- cated in the literature. The idea is that an offer supported by an argument has a better chance to be accepted by another agent. Unfortunately, a little has been done on showing how a new argument may change the status of an offer for an agent. In other words, how an acceptable (resp. rejected) offer becomes rejected (resp. accept- able) for an agent when he receives a new argument from another agent.In this paper, we assume that each negotiating agent is equipped with a particular argument-based decision system. This system assigns a status to each offer on the basis of the acceptability of their supporting arguments. We will study under which conditions an offer may change its status when a new argument is received and under which conditions this new argument is useless. This amounts to study how the accept- ability of arguments evolves when the decision system is extended by new arguments.