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Let B(H) be the C?-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B(H) preserving the star partial order in both directions if and only if one of the following assertions holds. (1) There exist a nonzero complex number α and two unitary operators U and V on H such that φ(X) = αUXV or φ(X) = αUX?V for all X ∈ B(H). (2) There exist a nonzero α and two anti-unitary operators U and V on H such thatφ(X)=αUXV orφ(X)=αUX?V for all X∈B(H).