The spin-S exchange interaction model of ferromagnetism is studied by the mean-field approximation. This model has 4S(S + 1) order parameters, and has infinitely many ground-state configurations. We define a single polarization parameter to describe the ordering of the system. Thermal variation of the polarization q(T) is determined for various spins. The phase transition is first order (except for S = 1/2) with phase transition temperature kT(c)/Jz = (2S - 1)/(4S ln2S), where z is the coordination number, and the discontinuity of q at T(c) is q(c) = (2S - 1)/2S.