In deformation twinning, twin boundaries (TBs) should coincide with the twinning plane. Here we show that the TBs of the most common twinning mode in hexagonal close-packed metals, {1 0 (1) over bar 2} , may not lie on the {1 0 (1) over bar 2} twinning plane. Examinations using transmission electron microscopy (TEM) reveal that the TBs in Co and Mg deviate significantly from the {1 0 (1) over bar 2} plane. High-resolution TEM confirms that the incoherent TBs entirely depart from the twinning plane with a magnitude greater than 45 degrees.