We describe a quantum wave packet method for computing the state-to-state quantum dynamics of 4-atom AB + CD -> ABC + D reactions. The approach is an extension to 4-atom reactions of a version of the reactant-product decoupling (RPD) approach, applied previously to 3-atom reactions (J. Chem. Phys. 2001, 114, 1601). The approach partitions the coordinate space of the reaction into separate reagent, strong-interaction, and product regions, using a system of artificial absorbing and reflecting potentials. It employs a partitioned version of the split-operator propagator, which is more efficient than partitioning the (exact) time-dependent Schrodinger equation. The wave packet bounces off a reflecting potential in the entrance channel, which generates a source term; this is transformed efficiently from reagent to product Jacobi coordinates by exploiting some simple angular momentum properties. The efficiency and accuracy of the method is demonstrated by numerical tests on the benchmark OH + H-2 -> H2O + H reaction.