The Wigner 9j-symbols are a generalization of Clebsch-Gordan coefficients and Wigner 3j- and 6j-symbols which arises in the coupling of four angular momenta. They can be written in terms of the Wigner 3j- and Wigner 6j-symbols. Let tensor operators T^(k_1) and U^(k_2) act, respectively, on subsystems 1 and 2.