Martensitic transformation of a Heusler-type Ni 2.18 Mn 0.82 Ga (subscripts indicate relative numbers of atoms) single crystal was observed by neutron diffraction and by white X-ray diffraction of synchrotron radiation with decreasing temperature. The single crystal shows a shape memory effect due to a thermo-elastic martensitic transformation at around 340 K. Both neutron and high intensity white X-ray beams are suitable for the observation of the transformation process, because neutron beam penetrates far into the material and the white X-ray beam exhibits many Laue spots simultaneouly. We observed the change of Laue spots during the transformation process. As a result, the single crystal shows a cubic Heusler structure at 400 K. One of the cubic axes is along the direction of crystal growth. In the process of decreasing temperature, the crystal divided into many small variants with tetragonal structures. Some of them have an axis, [1 0 0], [0 1 0] or [0 0 1], along the direction of crystal growth. The others are made by rotating the unit cell around a 1 1 1 axis of cubic structure or by forming the twin of these rotated unit cells. An angle of rotation is at most a few degrees. At 103 K the transformation is almost complete and many tetragonal structures are rearranged into several tetragonal structures, the axes of which, [1 0 0], [0 1 0] or [0 0 1], are along the direction of the crystal growth.