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This paper proposes a new motion-compensated frame interpolation (MCFI) method. The performance of MCFI is highly dependent on the accuracy of the estimated motion vectors (MVs). The proposed iterative motion estimation (ME) method estimates reliable MVs using linearity checking and restricted search areas. An adaptive interpolation method is also proposed to obtain MVs for blocks that do not have reliable MVs in the iterative ME process. The experimental results show that the proposed method outperforms the conventional MCFI methods in terms of the quality of the interpolated frames. Furthermore, the MVs from the proposed method are more accurate than those from the conventional methods.