The appearance of intensity spikes in measurements is a common problem in fluorescence correlation spectroscopy (FCS) studies of biological samples. In this work, we present a new method for generating artifact-free correlation curves from fluorescence traces that have undergone spike removal. This method preserves the temporal information throughout the measurement and properly represents the correlation between events separated by removed spikes. The method was validated using experimental data. The proposed algorithm is demonstrated herein to be generally applicable, but it is particularly powerful for cases where spikes occur frequently.