Laminar flame properties such as the laminar burning speed and Markstein length are important fundamental parameters which are useful for modeling turbulent flames, flame stabilization, and flammability limits. However, the experimental determination of these parameters is usually complicated by the presence of flame stretch, and extrapolation is needed to determine the unstretched flame speed and Markstein length. Often this extrapolation is carried out linearly, but for highly stretched flames a nonlinear extrapolation may be required. This paper proposes a new procedure for non-linearly extrapolating the laminar flame properties from experiments with spherically expanding flames; the procedure involves a least-squares fit of the experimental data (flame radius vs. time) onto a non-linear relation- ship between flame speed and stretch rate. The performance of this method is evaluated using synthetic data over a wide range of laminar flame speeds and Markstein lengths. The procedure is shown to be computationally inexpensive and robust, exhibiting insensitivity noise.