1. An apparatus for generating a dot signal for a plurality of color separations to record a halftone image of each color separation, comprising: area dividing means for dividing a whole image area into a plurality of image areas; screen angle assigning means for assigning a set of screen angles for said plurality of color separations with respect to each of said plurality of image areas; a first memory for storing a plurality of color-separated image signals for said plurality of color separations, said plurality of color-separated image signals representing a color image in said whole image area; a second memory for storing a plurality of screen pattern data for said plurality of color separations; selection means for selecting one of said plurality of screen pattern data for each color separation in each of said plurality of image areas according to said assigned set of screen angles assigned to each of said plurality of image areas; and a dot signal generator for comparing the selected screen pattern data with the color-separated image data for each separation, to thereby generate a dot signal for recording a halftone image of each color separation, wherein said plurality of color separations include four color separations for yellow, magenta, cyan and black inks and said apparatus, further comprising: a third memory for storing reference data assigned to an overlapping area, the overlapping area being formed between first and second image areas so that a density of each of four color separations of said overlapping area is equal to one of the first and second image areas, said reference data indicating, with respect to each of the magenta and cyan separations, which one of the two screen angles for the first and second image areas is used as a screen angle of the overlapping area.