A new selected area electron diffraction(SAED) pattern was found from Fe-illite. The lattice of the ED pattern can be described as a compound tessellation of{3,6}[79{3,6}] which is based on a large coincidence-site lattice (CSL)with oriented crystal associations rotated by a non-crystallographic angle 26°.This phenomenon corresponds to the plesiotwinning of Fe-illite and has been never repoted in the nature so far.