The Li-6(Li-6,alpha alpha)He-4 three-body reaction has been studied in a kinematically complete experiment at E-6Li = 6 MeV, from which indirect information on the H-2(Li-6, alpha)He-4 two-body reaction at 13 less than or equal toE(c.m.) less than or equal to 750 keV has been extracted by applying the Trojan horse method. The method used a recent improved formulation. The derived astrophysical S(E) factor for the two-body process is compared with that obtained from direct experiments.