Currently, the differential function has been widely used in power transformer protection, leading to a reliable discrimination between internal faults and other events. However, the conventional differential protection function based on the estimation of the current phasors presents difficulties in the detection of some internal faults, such as turn-to-turn faults and turn-to-earth faults close to the transformer neutral, and dependence on the harmonic restraint and harmonic blocking functions in maintaining protection scheme security during inrush conditions and external faults with CT saturation. In order to improve the performance of the traditional methods, a negative-sequence differential element with high sensitivity has been used in association with the commom harmonic blocking and harmonic restraint. However, internal faults and other disturbances associated to the power transformer protection present transients, which can be properly detected by using the wavelet transform. This paper proposes to recreate the traditional phase and negative-sequence current differential elements by using the boundary discrete wavelet transform of the currents flowing through the secondary winding of the differential CTs. The proposed method will be evaluated from extensive simulations of internal and external faults, and transformer energizations as well. It will also be evaluated the behavior of the method in the presence of CT saturation and transformer overexcitation, the time delay obtained in the internal fault detection, and the computational burden obtained in a real-time application.