We report here our preliminary results on orientation determination and phase identification using the electron backscatter diffraction (EBSD) technique. Using a scanning electron microscope (SEM) equipped with the EBSD attachment. it is now possible to study the correspondence and orientation relationships of parent-phase and martensite variants in shape memory alloys (SMAs). Previously, such an information was obtained from large single crystals studied by micro-beam X-ray Laue diffraction and supplemented by transmission electron microscopy study of thin foils. Figs. 1(a), (b) and (c) are three EBSD patterns taken from neighboring areas in a Cu-12.55Al-4.86Ni (wt%) SMA. Computer simulation reveals that Fig. 1(a) belongs to the parent-phase of D03-structure type, and Figs. 1(b) and (c) belong to variants A and D of 2H martensite, respectively. Corresponding simulated EBSD patterns are shown in Figs. 1(d), (e) and (f). Fig. 1 indicates that the (0 0 2)A basal plane of the martensite variant A is transformed from the (-2-2 0)p plane of the parent-phase and its [0-1 0]A direction from the [0 0 1]P direction. The (0 0 2)D basal plane of the martensite variant D is transformed from the (2-2 0)P plane of the parent-phase and its [0 1 0 ]D direction from the [0 0 1]P direction.