Résumé : The present study provides a fundamental understanding of the crystallography and the microscale behavior of the V-enriched and Al-depleted α’ martensite taking place during the microstructure formation and the deformation of the dual phase α + α’ microstructure produced in Ti-6Al-4V. This particular microstructure exhibits much larger work-hardening capabilities than the conventional wrought product. The as-quenched structure of the martensite is analyzed using the Phenomenological Theory of the Martensite Crystallography (PTMC) coupled with EBSD analyses. This approach sheds new light on the microstructure configuration obtained during the dual-phase treatment and its fine-scale mechanical behavior. The martensite preferentially forms into parallel groups of 3 self-accommodating variants separated by a misorientation of 63.26∘/[10¯553¯]α’. TEM analyses additionally show that the variants of a same group are separated by a hitherto unobserved {134¯1}α’ type twin plane. Postmortem analyses after tensile testing demonstrate that this twinning plane is mobile under deformation. This allows the martensitic microstructure to exhibit the remarkable property to reorient under uniaxial tension. This unique property is shown to be intimately related to the mobility of the {134¯1}α’ twinning plane thereby evidencing for the first time that twin boundary motion is not uniquely associated to the orthorhombic α’’ martensite but can also occur in hexagonal α’ martensite. Quantification of the Interaction Energy (IE) appears relevant to rationalize and predict the reorientation of the martensite. The critical influence of the parent β grains texture on the reorientation is evidenced, while the impact of this deformation mechanism on the ductility of the martensite is debated.