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The statement of the problem of a binary classification by precedents using formal concept lattices is given, in which the initial data are two binary contexts. It is specified that this problem is intractable due to the high computational complexity of discovery process of the formal concept and constructing for them of the lattices. The decomposition reception, which allows reducing the computational complexity of this process is proposed and theoretically justified. The reduction of computational complexity is achieved by separation of every initial context on polynomial number of boxes (subcontexts), followed by a search of the formal concepts in each selected box. The results of computational experiments are presented and they confirm the effectiveness of the proposed of reception of the reducing computational complexity.

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