The brain is a dynamic biosystem where the regions communicate with each other in a time-varying and adaptive way. Recently, abnormally varied brain statuses in brain diseases have been demonstrated with dynamic functional connectivity (FC) and a newly developed technique, high-order FC, which measures synchronization of the FC dynamics, providing a valuable way to characterize high-level brain function. However, there is a lack of method in quantification of local synchronization of the FC dynamics, another important facet of the high-level brain functional organization that could underpin complex regional brain activities. To this end, we propose a new method called high-order regional homogeneity (high-order ReHo) to evaluate such complex organizations of the local FC dynamics. We demonstrated that such a metric is more sensitive compared to the traditional low-order ReHo approach in individualized depression classification.