The local crystallography within shear bands (SB) has been examined in a single crystal of {112}< 111 > orientation of pure copper deformed at 77K by channel-die compression to strains of about 1. Setting up a system for making high-resolution orientation maps using transmission electron microscopy (TEM) has opened new advantageous circumstances for the analysis of orientation changes within SB. This method with spatial resolution higher than 10nm allows the examination of microstructure images composed of nanoscale subcells forming SB. It has been found that for well-developed shear bands, a crystal lattice rotation about < 112 > direction tends to dominate and this process is usually accompanied by activation of new slip systems. The present work shows that despite the plane strain deformation mode, the mechanism of lattice rotation within emerging SBs may lead to Goss and Brass texture components.