A new time-dependent wavepacket method is developed to study the A + BC -> AB + C, AC + B reaction at the state-to-state level. The method only requires propagation of the wavepacket in reactant Jacobi coordinates by extracting S-matrix information on a dividing surface right before the absorption potential in the product region. It has particular advantages for reactions with deep wells and long-range attractive interactions in the product channels in which the wavepacket in the product channels can only be absorbed sufficiently far away from the interaction potential. Demonstration made on the benchmark H + H-2 reaction shows that the method is rather efficient in dealing with a direct reaction at high collision energy. The method is applied to study the very challenging H + O-2 (v(0) = 0, j(0) = 0, 1) reaction, with state-to-state differential cross sections obtained for the first time for collision energies up to 1.1 eV. The calculations not only show the power and accuracy of the new approach in dealing with complex-forming reactions but also shed light on the dynamics of the H + O-2 reaction.