The state-to-state asymptotic analysis of tetraatomic reactions is presented. It is assumed that the four-atom time-independent partial wave Schrodinger equation has been solved subject to the condition that in the limit of very compact geometries the wave function vanishes. These solutions are initially obtained in body-fixed row-orthonormal hyperspherical coordinates and transformed in the asymptotic arrangement channel regions of nuclear configuration space to Jacobi body-fixed coordinates. From the latter, compact explicit expressions for the reactance (R) and scattering (S) matrices, useful for accurate numerical calculations, are obtained. The different systems of coordinates used and their interrelations are given. The approach described is particularly well suited for implementation on massively parallel architectures and is appropriate for the calculation of benchmark-quality state-to-state integral and differential cross sections on currently available computers.