An arrangement of magnetic liners for the bit lines or word lines of an MRAM device that reduces or eliminates stray magnetic fields at the ends of the magnetic liners, thereby reducing the occurrence of offset fields over portions of the MRAM device due to the magnetic liners is described. The orientation of magnetization of adjacent magnetic liners is alternated, causing the end poles of the magnetic liners to cancel each other. The shapes of the ends of the magnetic liners are alternated to vary their switching fields. Methods are described that use this ability to vary the switching fields to alternate the orientation of magnetization of the magnetic liners.