The angular correlations between the first-excited-state alpha particles from the C13 (He3, α) C12 reaction and the subsequent 4.43 MeV gamma rays have been studied as functions of the angle of emission of the gamma rays for alpha particles emitted at laboratory angles of 10°, 25°, 40°, 90° and 128° at a bombarding energy of 4.50 MeV. The correlation functions have been fitted with an expression of the form W(θγ) = 1 + b2 cos 2(θγ − θ2) + b4 cos 4(θγ − θ4).The cos 4θ term dominates the correlation function at low angles and the θ4 phase angle remains constant, while the θ2 phase angle behaves similar to the recoil axis at low angles. The behaviour of the cos 4θ term is inconsistent with a pickup model for the reaction. Other possible direct-exchange interaction models are discussed.