The classical three-point method for obtaining a diffusion coefficient of probes from the fluorescence recovery function in the Fluorescence Recovery After Photobleaching (FRAP) technique, when Gaussian or uniform spot-photobleaching profiles are used, leads to an expression that is not suitable for linear fittings. Therefore, determination of the diffusion coefficient is complex and very dependent on the recovery time. In this work we propose a new solution for the fluorescence recovery function after spot-bleaching using a Gaussian beam, which is a better alternative method than the three-point method for the data analysis of the FRAP kinetics. The new method can be applied for shorter recovery times thereby minimizing errors due to convective effects. It leads to a linear relationship between the recovery function and the diffusion coefficient and, as shown in the analysis of a model case, allows a more accurate determination of the diffusion coefficient of fluorescent probes.