The transformation texture associated with martensite formation in the titanium alloy Ti-6A1-4V has been investigated. Samples were heated into the fully P phase and quenched to form a microstructure of very fine alpha' martensite with no evidence of diffusional transformation at the prior beta grain boundaries. EBSD texture measurements on the martensite showed that within each prior beta grain, although typically all 12 variants of alpha' were formed, the fractions of variants was far from uniform. The alpha' texture was markedly different from values calculated using equal variant probability, also indicating that significant variant selection was occurring during martensitic transformation. This effect was modelled on the basis of elastic interaction between martensite events.