The purpose of the paper is to describe the solution to the quantum Yang–Baxter equation associated with the 8-dimensional spin representation Tsp of U q (s o 7) . The self-duality of Tsp and the symmetry of the corresponding braiding matrix are proved. Also, the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.