A process for resolving cognitive conflicts among group members with the help of cognitive maps and a group support system has been proposed. Cognitive conflicts have been studied in the context of Social Judgment Theory. The model involves a set of criterion events, a set of cues, and a set of judgments about those events, based on observation of those cues, by a set of judges. Disagreement arises because the judges fail to understand each other’s judgment making policies. Cognitive maps, which are designed to capture the structure of a person's causal assertions, can be used as a cognitive feedback mechanism that makes a decision-maker aware of his own cognitive orientation as well as that of others and help reduce differences. Since group support systems have been successfully used to manage conflicts, it is proposed to use the cognitive mapping technique within the purview of a group support system. A set of hypotheses are proposed to test the effect of the proposed process on the group’s judgment-making capability.