In this letter we propose a new fast matching algorithm that has no degradation of predicted images such as found in the conventional full search (FS) algorithm, so as to reduce the amount of computation of the FS algorithm for motion estimation in real-time video coding applications. That is, our proposing algorithm reduces only unnecessary computations in the process of motion estimation without decreasing the prediction quality compared to the conventional FS algorithm. The computational reduction comes from rapid elimination of impossible motion vectors. In comparison to the FS algorithm, we obtained faster elimination of inappropriate candidate motion vectors using efficient matching units based on image complexity. Experimentally, we demonstrated that the unnecessary computations were removed by about 30% as compared to the other fast FS algorithms.