It is shown by a crystallographic etching technique that deformation banding is an important deformation mode in copper. In a cold rolled coarse grain copper, deformation banding forms in a three dimensional manner dividing grains into a large number of bands of different orientations. The influence of this important, but long ignored deformation mode, is studied by incorporating it into the Taylor model. The predicted textures from the new model are better than those from other existing models in mainly two aspects. Firstly, the present model predicts the co-existence of the three major FCC rolling texture components, namely (123) or S component, (112) or C and (110) or B. The existing models are deficient in that they predict either C and S or B, but not their co-existence. The second point is that textures predicted by the existing models are always too sharp compared to the experimental textures. The deformation banding model predicts texture peaks with larger spread and hence more realistic texture sharpness.