For single intermediate enzyme kinetic systems, a relationship between a defined dimensionless parameter alpha (alpha) and the rate constants and initial enzyme concentration of the system was derived to describe the stationary-state trajectory of d(P)/dt versus (S) between the upper and lower bounds of the Michaelis-Menten and Briggs-Haldane systems. It was found that a is a function of E-o/k(m) and the parameter Omega, which is a function of k(2) and k(3). The development of the alpha parameter provides a new method for directly estimating all the rate constants in the enzyme kinetic model, given (S) and (P) data as a function of time. This method for estimating the three rate constants and initial enzyme concentration is tested on four sets of simulated discrete ( isothermal) data covering a range of different trajectories and on experimental data for the horseradish-peroxidase enzyme system.