The development of the constructive approach in the field of philosophy, pedagogy and psychology, as well as essential progress in the development of communication and information theory, emergence of the Internet and artificial intelligence systems, makes the use of the constructive approach in mediation relevant to date. On the basis of theoretical analysis of constructive approach and practical mediation experience of the authors, the general scheme of construct formation in the process of cognition and communication is described and the constructive mediation scheme is proposed. Attempts to analyse and generalize different theories are made providing those theories have different definitions of the same concepts, and also considering the decreasing efficiency of formal institutions in management of the society. The difference of constructive mediation presented in the charts is: the use of dialogue and its varieties of discourse in the process of mediation, training of the conflict parties to dialogue and organization of the discourse by the mediator; assistance to participants in the conflict in achieving the unambiguity of the representation of signs, which are used in communication by mediation participants; the formation and updating of constructs that promote consensus achievement; testing (questioning) of mediation participants and processing of results. Dialogue (discourse), training of conflict parties by a mediator, is considered as the key feature of the constructive approach in mediation. Gained results and its further methodological study will allow to develop the theory of mediation in the unified way, train participants of the mediation to gain dialogue and discourse skills and to reach consensus, allowing them to avoid new conflicts. Additionally, it would help to train mediators and other professionals who encounter conflicts between people in their official duties.