1. A threshold matrix generating method of generating a threshold matrix which is compared with a grayscale original image in halftoning said original image, comprising the steps of: a) providing a computer having a processor; b) sequentially assigning a plurality of linear areas, which are arranged in an arrangement direction without spaces in a matrix area, to a plurality of element groups along said arrangement direction, said matrix area being an area where a threshold matrix is generated and a plurality of elements are arranged in a row direction and a column direction, each of said plurality of linear areas extending in a tilt direction tilted relatively to said row direction and said column direction, said arrangement direction being perpendicular to said tilt direction, said plurality of element groups corresponding to a plurality of grayscale ranges acquired by dividing a whole grayscale range; c) specifying arbitrary one element in each element group to change said one element to a specified element and subsequently repeating a process of changing another element in said each element group to a specified element, said another element being farthest from specified elements in said each element group, on the premise of spatial repetition of said threshold matrix in halftoning of an original image, or repeating said process in accordance with a predetermined condition, to determine a turn-on order in which halftone dots are added to elements in said each element group in accordance with increase in gray level in a grayscale range corresponding to said each element group or a turn-off order in which halftone dots are removed from elements in said each element group in accordance with decrease in gray level in said grayscale range; and d) determining a threshold value of each element in said matrix area in accordance with a turn-on order(s) and/or a turn-off order(s) for said plurality of element groups; wherein said steps (b) to (d) are performed in said computer by said processor.