This paper proposes a new fault location method in radial medium voltage distribution networks. The proposed method only uses the measurement data at the feeder beginning to approximate the characteristic equation showing the dependence between the positive-sequence voltage and phase angle at the monitoring point with the distance to the fault location for each fault type on each line segment. To determine these characteristic equation coefficients, the entire distribution network will be modeled and simulated by four types of faults at different locations along the lines to build the initial database. Based on this database, the mathematical functions in MATLAB software are applied to approximate these coefficients corresponding to each type of fault for each line segment in the network. Then, from the current and voltage measurement data at the feeder beginning, the algorithms of global search, comparison, and fault ranking are used to find out where the fault occurs on the distribution network. Two types of distribution network with and without branches are studied and simulated in this paper to verify and evaluate the effectiveness of the proposed method.