Since Adrian Brown and Victor Henri's work, the simplest enzyme kinetics model, which contains only three rate constants k(1), k(2) and k(-1) in 1902, has been thoroughly explored in many directions. By using the Michaelis-Menten equation, K-M and k(2) can be measured quickly. All the three rate constants can be derived by temperature jump method or transient state kinetics, but both methods need more complicated techniques and equipments. In our previous paper (Li et al. in J Math Chem 46: 290-301, 2009), we gave a method to measure all the rate constants which does not require any additional equipment other than those needed for measuring K-M and k(2). Here, we propose a new one which needs no additional equipment either. This method is based on a study of inflection points of integral curves. Numerical results show that the new one is much better than the previous one in two aspects: near the end of the reaction, the new one gives more accurate estimation; during the quasi-steady state of the reaction, it also gives good estimations while the previous one can not. Hence, this method not only advances the estimation accuracy, but also has more choices for measuring.