Motif discovery is one of the fundamental problems in the signal detection and gene regulation. Motif discovery in biology is equivalent motif search and de novo motif finding problems in computer science. The challenging problem for both of these cases is Motif Representation (MR). A Common Position Weight Matrix (CPWM) is a simple MR model in which each position is independent from the other positions. However, the CPWM model is not an appropriate MR model. In fact, biological experiments show that the structural information is extremely important in motif discovery. The structural information is included in an MR model by considering dependent and conserved positions. Recently, some MR models have been introduced based on this assumption. These MR models are used only for the motif search problem.In this paper, we design a new MR model based on information theory. This model can be used for the de novo motif finding and motif search problems. We extract some known motifs from JASPAR and TRANSFAC databases to search for common features among them. Based on these features, a new MR model is constructed called EPWM. A jackknife test is used to show the EPWM model is more successful than the other MR models for the motif search problem. The jackknife test with each MR model (the EPWM model and the other MR models) is implemented and performed on the JASPAR and TRANSFAC databases. To verify the efficiency of the EPWM model for the de novo motif finding problem, we implement the EPWM model and the other MR models in the Gibbs sampling method. Finally, the Gibbs sampling method is …