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Human motion prediction is challenging due to the complex spatiotemporal feature modeling. Among all methods, graph convolution networks (GCNs) are extensively utilized because of their superiority in explicit connection modeling. Within a GCN, the graph correlation adjacency matrix drives feature aggregation and is the key to extracting predictive motion features. State-of-the-art methods decompose the spatiotemporal correlation into spatial correlations for each frame and temporal correlations for each joint. Directly parameterizing these correlations introduces redundant parameters to represent common relations shared by all frames and all joints. Besides, the spatiotemporal graph adjacency matrix is the same for different motion samples and cannot reflect sample-wise correspondence variances. To overcome these two bottlenecks, we propose dynamic spatiotemporal decompose GC (DSTD-GC), which only takes 28.6% parameters of the state-of-the-art GC. The key of DSTD-GC is constrained dynamic correlation modeling, which explicitly parameterizes the common static constraints as a spatial/temporal vanilla adjacency matrix shared by all frames/joints and dynamically extracts correspondence variances for each frame/joint with an adjustment modeling function. For each sample, the common constrained adjacency matrices are fixed to represent generic motion patterns, while the extracted variances complete the matrices with specific pattern adjustments. Meanwhile, we mathematically reformulate GCs on spatiotemporal graphs into a unified form and find that DSTD-GC relaxes certain constraints of other GC, which contributes to a better representation capability. By combining DSTD-GC with prior knowledge, we propose a powerful spatiotemporal GCN called DSTD-GCN, which outperforms SOTA methods by $3.9\% \sim 8.7\%$ in prediction accuracy with $55.0\% \sim 96.9\%$ fewer parameters.