We present the results of a new calculation of the electronic structure of the (001) surface of Cu, obtained by using the layer method and a tight-binding description of the electron states. The selfconsistency requirements arising from the surface charge transfer are treated by assuming a charge and configuration dependence of the intraatomic matrix elements. It is found that, at variance with what obtained for other transition metals, the self-consistency plays a crucial role in determining the nature and the location of the surface states. A detailed discussion of the main surface features in the layer band structure and in the local densities of states at the topmost layers is given together with a comparison with previous theoretical work. The results are discussed in the light of the available experimental data.