Detecting the sites on genomic DNA at which DNA binding proteins bind is a highly relevant task in bioinformatics. For example, the binding sites of transcription factors are key elements of regulatory networks and determine the location of genes on a genome. Usually, for a given DNA binding protein, only a few DNA-subsequences at which the protein binds are known experimentally. The task then is to deduce the global binding characteristics of the protein based on these few positive examples. A widespread approach is the so-called profile-matrix (PM). The PM-approach can be interpreted as a linear classifier (binding word class/non-binding word class) within the space of sequence words, with the profile of the experimentally verified binding sites determining its parameters. In this paper a novel approach called binding-matrix (BM) is introduced. Like the PM, the BM realizes a linear classification, but in contrast to the profile-matrix approach the parameters (matrix) of the classifier is now determined by maximum likelihood estimation. Tested on data from the TRANSFAC database, the maximum likelihood estimation leads to an increase in classification performance by about an order of magnitude.