We present a computational method for the calculation of quantum state-to-state reactive probabilities for reduced dimensionality, three degree-of-freedom, AB + CD <----> A + BCD reactions. Our approach is based on the recently developed wave packet propagation method in real L-2 eigenstates [Skokov, S.; Bowman, J. M. Phys. Chem. Chem. Phys. 2000, 2, 495]. Here we show how the real L-2 approach can be used for the calculation of state-to-state probabilities. The "coordinate transformation problem" is relatively easily solved in the L-2-eigenstate formulation because the eigenstates used for propagation are analytical functions of the coordinates. The method is tested for the H-2 + CN <----> H + HCN reaction for zero total angular momentum, J, using a previous potential energy surface of Sun and Bowman, who reported reduced dimensionality, time-independent calculations of state-to-state reaction probabilities. New calculations for J > O are presented using the adiabatic rotation approximation. In this approximation the L-2-eigenstates are obtained efficiently by expanding them in the basis of J = O eigenstates. Finally a test of J-shifting is done.