This paper proposes a modified current differential relay for $Y-{Delta}$ transformer protection. The relay uses the same restraining current as a conventional relay, but the differential current is modified to compensate for the effects of the exciting current. A method to estimate the circulating component of the delta winding current is proposed. To cope with the remanent flux, before saturation, the core-loss current is calculated and used to modify the measured differential current. When the core then enters saturation, the initial value of the flux is obtained by inserting the modified differential current at the start of saturation into the magnetization cure. Thereafter, the core flux is then derived and used in conjunction with the magnetization curve to calculate the magnetizing current. A modified differential current is then derived that compensates for the core-loss and magnetizing currents. The performance of the proposed differential relay was compared against a conventional differential relay. Test results indicate that the modified relay remained stable during severe magnetic inrush and over-excitation, because the exciting current was successfully compensated. This paper concludes by implementing the relay on a hardware platform based on a digital signal processor. The relay does not require additional restraining signal and thus cause time delay of the relay.