In [A.A. Stolin, On rational solutions of Yang–Baxter equation for sl ( n ) , Math. Scand. 69 (1991) 57–80; A.A. Stolin, On rational solutions of Yang–Baxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533–548; A. Stolin, A geometrical approach to rational solutions of the classical Yang–Baxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347–357] a theory of rational solutions of the classical Yang–Baxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g . We prove that up to gauge equivalence all rational solutions have the form X ( u , v ) = Ω u − v + t 1 ∧ t 2 + ⋯ + t 2 n − 1 ∧ t 2 n , where Ω denotes the quadratic Casimir element of g and { t i } are linearly independent elements in a maximal torus t of g . The quantization of these solutions is also emphasized.