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In recent years, high bit-depth (HBD) images with 10 [bits/channel] or more are being used more often for their improved image quality. However, the size of HBD images become large and so more effective encoding techniques are needed. This paper considers the bit-depth transform process from the view point of minimizing bit-depth transform error. The minimization method is designed according to an optimum quantization algorithm. As a result, our method can improve the coding efficiency by an average of 11 [%] compared to the conventional method with AVC/H.264.