In this study, a hyperbolic S-transform-based method is proposed to discriminate most important transient fault currents of transformers. First, the proposed method discriminates external faults from other disturbances. Then, the S-transform is applied to differential currents. An index is suggested by using absolute deviations of the S-matrix of differential currents to discriminate internal incipient faults in addition to inrush currents and internal faults. The relay issues an alarm signal in the case of the incipient fault but restrains during the magnetising inrush current. If an internal fault is recognised, the relay will issue a trip signal. To study the robustness of the suggested method, a program is developed in the MATLAB environment. The inputs of this program are differential current signals, derived from a system modelled by EMTP software. In order to simulate the internal incipient fault along with internal turn to turn and turn to earth faults, the transformer is modelled as 8 × 8 RL matrices, derived by using subroutine BCTRAN in EMTP. Also, differential currents are contaminated by noise and it is shown that the suggested method is not affected by noise and it can discriminate incipient faults, inrush currents, internal faults and external faults.