This paper presents a new two-terminal numerical algorithm for fault location estimation and for faults recognition using the synchronized phaser in time-domain. The proposed algorithm is also based on the synchronized voltage and current phasor measured from the assumed PMUs(Phasor Measurement Units) installed at both ends of the transmission lines. Also the arc voltage wave shape is modeled numerically on the basis of a great number of arc voltage records obtained by transient recorder. From the calculated arc voltage amplitude it can make a decision whether the fault is permanent or transient. In this paper the algorithm is given and estimated using DFT(discrete Fourier Transform) and the LES(Least Error Squares Method). The algorithm uses a very short data window and enables fast fault detection and classification for real-time transmission line protection. To test the validity of the proposed algorithm, the Electro-Magnetic Transient Program(EMTP/ATP) is used.