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The notions and algorithms of generating basis for exactness rules and the proper basis for conditional rules of redescription database are presented using closure operator of Galois connection based on the operations of formal concept analysis (FCA). It is demonstrated that constructed rules of redescription database are minimal non-redundant. At the same time, a new algorithm, i.e. non-redundant rules method (NRRM), is employed to discover minimal non-redundant exactness, and the conditional rules are addressed. In addition, part numerical computation program and detailed resolution of NRRM algorithm are presented to verify the proposed theorem. It is found that the theorem has good application to practical cases.