Abstract. This note studies the iterative solution to the coupled quaternion matrix equations [ ∑ i=1 p 𝕋 1i ( X i ), ∑ i=1 p 𝕋 2i ( X i ),⋯, ∑ i=1 p 𝕋 pi ( X i ) ]=[ M 1 , M 2 ,⋯, M p ] , where ...