The complex and intricate microstructure of B19’ martensite in shape memory nickel titanium alloys is generally explained with the Phenomenological Theory of Martensitic Crystallography (PTMC). For the last decade, we have developed an alternative approach that supposes the existence of a “natural” parent-daughter orientation relationship (OR). As the previous TEM studies could not capture the global crystallographic characteristics of the B2-B19’ transformation required to discriminate the models, we used Electron BackScatter Diffraction (EBSD) and Transmission Kikuchi Diffraction (TKD) to investigate a polycrystalline NiTi alloy constituted of B19’ martensite. The EBSD maps show the large martensite plates and reveal a coexistence of different ORs. The TKD maps permit to image the “twins” and confirm a continuum of orientations. The results are interpreted without PTMC, with anew hypotheses. The predominant OR in EBSD is the “natural” OR for which the dense directions and dense planes of B2 and B19’ phases are parallel, i.e. (010)_B19’ // (110)_B2 & [101]_B19’ // [ -111]_B2 . The natural OR was used to automatically reconstruct the prior parent B2 grains in the EBSD and TKD maps. From the distortion matrix associated to this OR, we calculated that the habit plane could be (1-12)_B2 // (10-1 )_B19’. The traces of these planes are in good agreement with the EBSD maps. We interpret the other ORs as “closing-gap” ORs derived from the natural OR to allow the compatibility between the distortion variants. Each of them restores a parent symmetry element between the variants that was lost by distortion but preserved by correspondence. The oral presentation is divided in three parts: 0-26 min : Introduction, some words about the limits of the PTMC, 26-50 min : Experimental EBSD and TKD Results, 50-80 min : Interpretations and conclusions. All the details can be found in https://doi.org/10.3390/cryst10070562.