An efficient and accurate wave packet method is proposed for the calculation of the state-to-state S-matrix elements in bimolecular reactions involving four atoms. This approach propagates an initial state specific wave packet in reactant Jacobi coordinates. The projection in product channels is carried out on projection planes, which have one less degree of freedom, by transforming both the time-dependent wave packet and final product states into a set of intermediate coordinates. This reactant-coordinate-based method is more efficient than product-coordinate-based methods because it typically requires a smaller number of basis functions or grid points and allows the determination of S-matrix elements for multiple product channels from a single propagation. This method is demonstrated in calculating the (Jtot = 0) state-to-state S-matrix elements for both the abstraction and exchange channels of the H + H2O reaction.