The application of the Nesbet algorithm to the full iterative solution of the two-dimensional master equation for thermal unimolecular reactions is presented. This leads to an efficient algorithm for computing thermal rate coefficients in the falloff regime for reactions such as simple fission dissociations, radical-radical recombinations, and ion-molecule reactions wherein microcanonical dissociation rate coefficients are sensitive to both the vibrational energy and the angular momentum of the excited species.