This paper proposes a propositional modal logic with a modality □φ=□₁V□₂φ, and specifies the language, the syntax and the semantics for the logic. The axiomatic system for □ is sound and complete, where □₁ and □₂ are given in this paper. The axiomatic system for the logic has the similar language, but has the different syntax and semantics. For any formula φ, □φ=□₁V□₂φ; the frame for the axiomatic system is defined as an tripleW,R₁,R₂, and the model is defined as quadruple W,R₁,R₂,I. When the completeness theorem is proved, two equivalence relations are constructed on the set that is made up of all the maximal consistent sets. The construction method of a canonical model for the axiomatic system is different from the classical canonical model. If the accessibility relation R₁ for □₁ is the accessibility relation R₂ for □₂, then the axiomatic system for □ changes into S5.