Individual institutions marginal contributions to the systemic risk contain predictive power for its potential future exposure and provide early warning signals to regulators and the public. We use higher-order co-skewness and co-kurtosis to construct systemic risk contribution measures, which allow us to identify and characterize the co-movement driving the asymmetry and tail behavior of the joint distribution of asset returns. We illustrate the usefulness of higher-order moment augmented approach by using 4868 stocks living in the Chinese market from June 2002 to March 2022. The empirical results show that these higher-order moment measures convey useful information for systemic risk contribution measurement and portfolio selection, complementary to the information extracted from a standard principal components analysis.