A new coupled-chemistry PNS solution technique is developed for predicting finite-rate chemically reacting flows over a wide range of Mach numbers and for altitudes ranging from sea level to 250 kft. New diagonalized, two-step, and strongly implicit solution schemes are developed to efficiently and accurately solve the coupled species conservation equations. Furthermore, a new quasisteady ablation model is developed for Teflon that accounts for the material density variations. Numerical tests are conducted over the Mach number range of 6.89-20 and altitude range from sea level to 250 kft, and comparisons are made with available wind-tunnel and flight data on surface heat-transfer rates. The results show that the new two-step solution scheme provides a uniquely attractive combination of accuracy, stability, and computational efficiency over the entire range of conditions tested. Furthermore, nonablating low-altitude calculations show that finite-rate chemistry effects are still significant over a major portion of the shock layer. The classical Blottner-type linearization of the production terms is unstable for low-altitude high-Reynolds-number conditions. The results of Teflon ablation calculations show that, for the altitude range of 75-250 kft, the predicted surface ablation rates using our quasisteady ablation model are within 10% of the predictions of Scala's correlation based on flight data.