1. An image processing apparatus which inputs and quantizes multivalued image data representing each color by plural bits into image data of a less number of bits, comprising: addition means for adding an error of each color occurred in previous quantization to the input multivalued image data of each color; and quantization means for converting the M (M&gE;2) multivalued image data after the addition obtained by said addition means into the data after the quantization of the respective colors, wherein, in an M-dimensional space formed by the M multivalued data, said quantization means performs the quantization process without considering correlation of the respective colors when the input multivalued image data is on a higher position in the space, and performs the quantization process as considering the correlation of the respective colors when the input multivalued image data is on a lower position in the space.