We can also coupled together four angular momenta. Consider two four-body states, with single-particle angular momenta \( j_a \), \( j_b \), \( j_c \) and \( j_d \) we can have a state with final \( J \) $$ |\Phi(a,b,c,d)\rangle_1 = | ([j_a\rightarrow j_b]J_{ab}\times [j_c\rightarrow j_d]J_{cd}) JM\rangle, $$ where we read the coupling order as \( j_a \) couples with \( j_b \) to given and intermediate angular momentum \( J_{ab} \). Moreover, \( j_c \) couples with \( j_d \) to given and intermediate angular momentum \( J_{cd} \). The two intermediate angular momenta \( J_{ab} \) and \( J_{cd} \) are in turn coupled to a final \( J \). These operations involved three Clebsch-Gordan coefficients.

Alternatively, we could couple in the following order $$ |\Phi(a,b,c,d)\rangle_2 = | ([j_a\rightarrow j_c]J_{ac}\times [j_b\rightarrow j_d]J_{bd}) JM\rangle, $$