In this contribution, a simple two-dimensional model of the DNA is presented. In this model the two polynucleotide strands are linked together through the hydrogen bonds which are described by the Morse potential. The longitudinal links between base pairs are described by anharmonic potential. The model predicts that an open state of the molecular chain in the form of nonlinear structure named cuspon, arise under certain conditions. We suggest that anharmonicity may play an important role in DNA denaturation.