We propose a method for calculating the unitary evolution matrix of the arbitrary spin-s operators rigorously. This is an indirect method, which differs from the method of group theory or the method of direct calculation. The kernel of our method is to use the identity of two systems in their expressions, namely the Hamiltonian Hs=Sx of spin-s particle and the Hamiltonian of the Heisenberg XX open chain with interaction J=n(N-n). Because of this identity, the calculation of the unitary evolution matrix of the spin-s operators is substituted by the calculation of the state evolution matrix in Heisenberg XX open chain. As examples, the unitary evolution matrix of s=3/2, s=2 and s=5/2 are calculated by using our method. Since the evolution of the state |sm〉 under the operator e-itSx corresponds to the rotation of the initial state |sm〉 around the x-axis by an angle β＝t, and the evolution matrix element dsm′m(t)=〈sm′|e-itSx|sm〉 is just the projection of the finial state e-itSx|sm〉 on the initial state |sm′〉, the evolution matrix at t=π corresponds the perfect transmission of quantum state in the Heisenberg XX open chain.