A novel identification criterion for transformer inrush current based on the decay rate of the ratio of aperiodic component and fundamental component (referred to as k0) is proposed. Under the no-load closing status of a transformer, the current only exists on the power source side, while under other operating conditions, the current exists on all sides. Therefore it is possible to make use of this difference to identify the no-load closing status first. In case of no-load closing status, the decay rate of k0 is then adopted to distinguish between inrush current and internal fault current. The simplicity of the proposed criterion in principle and computation enables its implementation in real-time applications. Simulation results by Matlab and the malfunction data on the field indicate that the proposed method can not only reliably block the protection when the transformer is in the ultra-saturation condition, but also provide a faster operation speed under slight internal faults, which is a beneficial complementary to the conventional second-harmonic criterion. This work is supported by National Natural Science Foundation of China (No. 51777071).