Let A i and B i , 1 ≤ i < n, be bounded linear operators acting on a separable Hilbert space H. In this note, we prove that sup{∥Σ n i=1 A i XB i ∥ X ∈ B(H),∥X∥ < 1} = sup{∥Σ n i=1 AiUB i ∥:UU* = U*U = IU ∈ B(H)}. Moreover, we prove that there exists an operator X o with ∥ X 0 ∥ = 1 such that ∥ Σ n i=1 A i X 0 B i ∥= sup{∥ Σ n i=1 AiXBi:X ∈ B(H), ∥ X ∥ ≤ 1} if and only if there exists a unitary U 0 ∈ B(H) such that || Σ n i=1 AiU 0 B i ∥ = supΣ n i=1 AiXBi∥: X∈B(H), ∥X∥≤1}.