Abstract I investigate the use of the SU(3) Clebsch–Gordan coefficients in light of the relations of completeness and closure. I show that in the case of α$_{V}$ = F/(F + D) ≠ 1, there is an additional interaction: the exchange of a ρ meson between a Λ and a Σ$^{0}$ hyperon that only affects the symmetric coupling. I then calculate these additional coupling constants and show that this recovers the completeness and closure of the SU(3) Clebsch–Gordan coefficients for all values of α$_{V}$. Besides, it increases the symmetry of the theory, now we can group the baryon octet into four doublets. Finally, I add the new coupling constants to study numerical results in the hyperon onset in dense nuclear matter assuming α$_{V}$ as a free parameter.