To further improve the performance of differential protection for power transformers, this paper presents a new method for distinguishing inrush currents from internal faults using the extreme values of current derivation rate. In the condition of inrush currents, there are at least one phase whose current waveforms have the characteristics of discontinuity and steeple wave and the time span between the maximum value and the minimum one of the derivation rate in a power frequency cycle is less than half a cycle. While in the case of internal faults, its derivation rate curve is close to sine waveform and the time span between the maximum value and the minimum one is approximately near to half a cycle. Using the current derivation rate, on the one hand, can weaken the impact of DC component. On the other hand, it can also highlight characteristics of the intermittent critical point. Thus, a criterion using the features of current derivation rate is developed and the corresponding realization flow is presented. At last, the results of dynamic tests under different conditions suggest that the proposed algorithm can identify inrush currents from internal faults in a power frequency period accurately and quickly, with clear principle, simple criterion, and a small amount of calculation. It also provides a helpful theoretical basis for improving the performance and optimization of differential protection in power transformers. This work is supported by National Natural Science Foundation of China (No. 51207119).