We present a theory that models the reflectance difference spectrum of bulk, spontaneously ordered Ga 0.5 In 0.5 P. Near the band gap E 0 this spectrum exhibits a sharp, negative feature at E 0 and a broad positive feature that peaks near E 0 ϩ⌬ S . The zero crossing between these two peaks occurs near E 0 ϩ⌬ C . For the sample studied in this paper, the spin-orbit splitting ⌬ s and the crystal-field splitting ⌬ C are 120 and 25 meV, respectively. Two previous calculations, which assume constant transition-matrix elements, were able to produce a negative peak at E 0 , but not the positive feature. In this paper, the reflectance difference spectrum near the band gap is calculated using an 8-band k•p model and an explicit treatment of the momentum or k dependence of the transition-matrix elements. The new calculation produces both the negative peak at E 0 and the positive feature that peaks near E 0 ϩ⌬ S . The positive feature is attributed to the strong k dependence of the matrix element anisotropy. A strong coupling, enhanced by ordering, between three valence bands is essential. A problem associated with the analytical expression for the dielectric function used in previous calculations is discussed. ͓S0163-1829͑97͒07224-X͔