1. A threshold matrix generation method of generating a threshold matrix for Nx speed writing to be compared with a multi-tone original image when said original image is screened into halftone dots for Nx speed writing by an image recording apparatus capable of recording an image at 1× speed or at Nx speed, where N is an integer of 2 or more, the method comprising: a) preparing a matrix space that is a set of matrix elements arranged in row and column directions, said row direction being perpendicular to said column direction, and said column direction corresponding to a recording direction of said image recording apparatus; b) setting every Nth matrix element aligned in said column direction and every Nth matrix element aligned in said row direction as writing elements and setting the other matrix elements as non-writing elements, said writing elements being matrix elements that correspond to writing positions on a recording object at the time of Nx speed writing; c) setting a first area and a second area, said first area being a cluster of a plurality of first partial areas that are substantially evenly distributed in said matrix space and each include a plurality of writing elements, and said second area being the area of said matrix space excluding said first area; d) changing at least two writing elements in each of said first partial areas into determined elements by first allocating an initial occurrence number to one writing element in said first area to determine said one writing element as a determined element and then, in consideration of repetitive application of said threshold matrix when performing screening of said original image, repeating processing for specifying a writing element that is distant from every determined element in said first area on the basis of a distance from said every determined element and for allocating the next occurrence number to the specified writing element to change the specified writing element into a determined element; e) after said operation d), changing at least one writing element in said second area into a determined element and then changing another writing element into a determined element by repeatedly specifying a writing element that is distant from every determined element on the basis of a distance from said every determined element and allocating an occurrence number to the specified writing element, in consideration of repetitive application of said threshold matrix when performing screening of said original image; and f) determining a threshold value of each writing element in accordance with said occurrence number to obtain a threshold matrix for Nx speed writing.