A method prints on a printing material using inks and dampening fluids. An ink printing machine uses ink print heads to apply an image to a front side of the printing material and a dampening fluid print head to apply a dampening fluid image, thus reducing or avoiding water-related cockling of the printing material. The method includes: providing the image to be printed, calculating n different color separation matrices, calculating n ink amount matrices An from the color separation matrices, and calculating a total ink amount matrix A. For every element of the total ink amount matrix: calculating a matrix B as B=G*A, with a weighting matrix G and determining the maximum of the matrix B, calculating a dampening fluid matrix C, calculating the dampening fluid image from the dampening fluid image matrix C, and printing the ink image and the dampening fluid image.