A new approach for differential protection based on the mother wavelets which match in shape with inrush and fault current waveforms is proposed in this work. It is demonstrated that if the matched wavelet is used for processing inrush and fault waveforms of transformer then its detection capability improves. In case of false tripping of transformer, the equipment is to be opened for inspection for faults. This leads to equipment outage because there is no mechanism to ascertain that there was no fault. It is needed that inrush and fault be detected independently not only for the purpose of faster and better detection but also for studying mal-operations and post-analysis. For a faster and better detection, a new protection scheme is also proposed making use of independent detection of fault and inrush waveforms. To find matched inrush and fault wavelets, differential evolution algorithm is used. Out of various possible solutions for different number of wavelet coefficients, a choice is made by further testing on various switching angles. The effectiveness of the proposed method is tested through PSCAD simulations on transformers of different ratings.