In our previous publication (Thermochim. Acta 222 (1993) 85), a computer algorithm was devised which allowed the concurrent determination of two rate constants, k(1) and k(2), for two consecutive irreversible first-order reactions. The Paradox 3.5 database was employed, and database analyses were carried out using both theoretical and experimental data. The k values obtained were in satisfactory agreement with assumed and observed values. In all the runs made, the values of k(1) were much larger than those corresponding to k(2). The preceding algorithm, however, did not hold for cases where k(2) was greater than k(1). The aim of the present paper is to modify the preceding script so that the resulting script will be applicable to both cases, k(1) > k(2) and k(2) > k(1). Limitations of the method will be described where applicable.