We report a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anticorrelated fluctuations under a noncorrelated noise background. Using this new method, by changing and scanning the start time and end time along a pair of fluctuation trajectories, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anticorrelated, or noncorrelated; after which, a cross-correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis. We specifically discuss an application of this approach to analyze single-molecule fluorescence resonance energy transfer (FRET) fluctuation dynamics where the fluctuations are often complex, although this approach can be useful for analyzing other types of fluctuation dynamics of various physical variables as well.