1. A method for producing half-tone reproductions of an original on a recording medium by means of a recording element using rotated screens having any screen angle and any screen line spacing and being formed of periodically repeated, adjacent screen grid elements comprising screen dots varying in size with the tone values of the original, comprising the steps of: (a) optoelectronically scanning said original line-by-line and dot-by-dot; (b) generating image values from the scanning representing the tone values of the original; (c) providing a matrix having a number of matrix elements, said matrix representing said periodically repeated grid elements; (d) generating a threshold value for each matrix element, said threshold values representing predetermined grey tone values, and said threshold values having amplitudes and a distribution in the matrix according to a predetermined function; (e) subdividing the recording medium into a plurality of adjacent areal elements which are aligned in scanning directions of the recording element and from which the screen dots of the rotated screen are built up inside each screen grid element; and (f) during recording medium scanning, generating a recording element recording signal for each areal element to form the screen dots inside the screen grid elements of the rotated screen by comparison of at least one image value with a threshold value of a matrix element whose location within said matrix corresponds to a respective location of said recording medium areal element within said screen grid element of the rotated screen and determining by said comparison of the threshold value and the image value whether the areal element is recorded or not when forming the screen dots.