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In recent years, as a promising option to improve the overall efficiency of energy utilization and absorptive capacity of renewable energies, the integrated energy system (IES) has raised great interest in academies and industries. Multi-energy flow (MF) calculation, which differs from the traditional power flow calculation, plays a basic role in analyzing IES. MF calculation based on Newton-Raphson method has been proposed in literature, but its calculation efficiency is not high. In this paper, a fast decoupled MF (FDMF) calculation method for IES is proposed. Its main idea is to replace the original Jacobian matrix of MF calculation based on Newton-Raphson method with a diagonal and constant Jacobian matrix by the transformation. The simulations demonstrate that the proposed FDMF method can increase the calculation efficiency by at least 4 times with high calculation accuracy.