Legacy differential protections are highly efficient and selective for high current and low impedance faults (LIF). In the case of high impedance faults (HIF), the differential and impedance protections lose that efficiency in detecting such events, and sometimes the failure evolves from a HIF fault to a LIF fault. This is due to the failure of the protection relay to detect these phenomena in certain power lines. This work presents a new sensitive algorithm for the detection of HIF combined with the differential line function in the time domain. The proposed solution is capable of detecting both LIF and HIF, by measuring and processing voltage and current signals. The efficiency of the novel approach relies on the classification techniques for instantaneous values.