Graphite fragments of nanometer size, called nanographite, have a different electronic structure than both bulk graphite and aromatic molecules. In particular, if they have zigzag edges, a sharp peak in the density of states at the Fermi level is generated, suggesting to cause Fermi instability. We have studied the lattice distortion and the possible magnetization based on the model of graphite ribbons with a nanometer width, by taking into account the electron-phonon and electron-electron interactions in the form of a tight binding model.