Magnetic shape memory effect is general name for several effects in which the most visible feature is huge strain induced by magnetic field. Magnetic field-induced structure reorientation (MIR) occurs due to motion of twin boundaries in single phase. As the magnetic field is a relatively weak force compared with mechanical stress, very high mobility of twin boundaries is crucial. Here we study the properties of martensite relevant for this effect using X-ray diffraction, optical and electron microscopy, magnetic observation and mechanical testing. In 10M modulated martensite, two types of mobile twin boundary (type I and type II) are observed with complex layered microstructures consisting of a hierarchy of twinning systems. We search for analogue with non-magnetic Cu-Ni-Al shape memory alloy.