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This paper proposes a new motion-compensated frame interpolation (MCFI) method. The proposed method utilizes a symmetric motion estimation (SME) method, which is a new pixel-wise motion estimation method for intermediate frame interpolation. By using an adaptive search range for the motion estimation, the proposed method can obtain a more reliable motion vector for each pixel than previous MCFI methods that use a conventional block matching algorithm (BMA). In addition, we propose a combined method of the SME and BMA to reduce the computation time of the pixel-wise motion estimation method. The experimental results show that the proposed method outperforms other MCFI methods in terms of generating objectively and subjectively better interpolated frames.