When a short-circuit fault with transition resistance occurs on a transmission line, it is difficult to derive the distribution coefficients if both ends of the transmission line are not synchronous. So, for the distance protection and fault location device, it is difficult to give an accurate analytical expression for the impedance measurement. For this problem, this paper aiming at the two-phase short circuit fault gives a set of analytical expressions for the impedance measurement. The simulation results prove that the analytical expressions are correct.