The fluorescence correlation spectroscopy (FCS) has become a powerful tool that entails the information about molecules at very minute concentrations in the biological system. With the advances in the laser technology and confocal microscopy, the applications of FCS have been extended to the studies of protein dynamics in living cells as well as drug-screening. Two assumptions are made in FCS: the biological system under study is in its equilibrium state and the molecules diffuse within the system freely according to Brownian motions. Fluorescence intensity fluctuations occur when the fluorescent molecule moving in and out of the confocal microscopy defined detection volume in which bursts of photons are emitted. Based on the assumptions above, the statistical-physics-based autocorrelation function of the fluorescence intensity fluctuations was formulated by Aragon and Pecora, which provides the information about the dynamics of the fluorescent macromolecules in the system. However, in this manuscript, we demonstrate that the temporal autocorrelation function of Aragon and Pecora was inadequately derived due to the fact that the process of the positions of a molecule in the system over time is not a stationary Gaussian process. Efforts are made here to derive a new version of the autocorrelation function of the temporal fluorescence intensity fluctuation. The fit of the new autocorrelation function will be compared with that of Aragon and Pecora.