1. An apparatus for decoding an image, the apparatus comprising: an entropy decoder that performs entropy decoding to generate quantized transformation coefficients of a transformation unit in a coding unit; and an inverse transformer that inverse quantizes the quantized transformation coefficients to generate transformation coefficients of the transformation unit and inverse transforms the transformation coefficients to generate residual components of the transformation unit, wherein, when a prediction mode is an inter prediction mode, not an intra prediction mode, a size of the transformation unit in the coding unit is determined independently from a size of a prediction unit in the coding unit, the image is split into a plurality of maximum coding units, according to information about a maximum size of the coding unit, the maximum coding unit is hierarchically split into one or more coding units of depth including at least one of a current depth and a lower depth, according to split information, when the split information indicates a split for the current depth, the coding unit of the current depth is split into four rectangular coding units of a lower depth, independently from neighboring coding units, and when the split information indicates a non-split of the current depth, the prediction unit is obtained from the coding unit of the current depth and the transformation unit is obtained from the coding unit of the current depth.