1. A halftone image generation method of generating a halftone image which is formed on a printing plate for letterpress printing, comprising the steps of: forming minimum halftone dots each of which consists of three or more pixels at predetermined halftone dot-central positions in a halftone area included in a halftone image generation space corresponding to a grayscale area included in a grayscale original image so that a density of minimum halftone dots is increased as a gray level of said grayscale area becomes higher, gray levels of said grayscale area being equal to or lower than a mode switching gray level which is determined, in advance, as a gray level close to the lowest gray level where any halftone dots do not exist; and forming halftone dots which grow from minimum halftone dots as a gray level of said original image becomes higher, at halftone dot-central positions in another halftone area included in said halftone image generation space corresponding to another grayscale area included in said original image, gray levels of said another grayscale area being higher than said mode switching gray level, wherein each of said minimum halftone dots comprises: a rectangular main cluster consisting of two or more pixels; and a sub-cluster located around said main cluster, the number of pixels of said sub-cluster being smaller than that of said main cluster, and said sub-cluster is one pixel or a plurality of pixels arranged approximately in a direction which extends from said main cluster, and only a vertex of said sub-cluster contacts with said main cluster or only a side of said sub-cluster contacts with a side of said main cluster, said side of said sub-cluster being shorter than said side of said main cluster.