Introduction The master equation theory of precompound and compound nuclear reaction has been generalized to the inclusion of the conservation of angular momentum and parity. Based on this improved semi-classical multi-step compound theory the Hauser-Feshbach and Exciton Model was unified, with which the code UNF has been developed as an evaluation tool of the calculations of nucleon induced reaction cross sections and double differential cross sections at incident neutron energies Introduction The master equation theory of precompound and compound nuclear reaction has been generalized to the inclusion of the conservation of angular momentum and parity. Based on improved semi-classical multi-step compound theory the Hauser-Feshbach and Exciton Model was unified, with which the code UNF has been developed as an evaluation tool of the calculations of nucleon induced reaction cross sections and double differential cross sections at incident neutron energies