Titanium alloys are widely used in various industrial, domestic, and medical applications such as turbine blades, bicycle frames, knee implants, etc. The two-phase titanium alloy Ti-6A1-4V (wt. percent) is considered to be a workhorse alloy for many applications in these diverse fields. Despite the large body of work on this alloy, the question of the transformation mechanism from the hcp a to the bee beta phase, occurring on heating to temperatures above the alpha/beta transus at similar to 980 degrees C, is still unresolved. Due to experimental difficulties, it has not yet been clearly determined whether the increase in beta volume fraction occurs by fresh nucleation of beta crystals within a phase grains or the growth of preexisting beta Mains. Since the Burgers orientation relationship holds only if the beta grains are nucleated within the a grains, the outcome of this question greatly affects texture-modeling efforts for this system. The Burgers orientation relationship predicts that the {0001} crystal direction in a grain of the a phase becomes a {110} crystal direction in a grain of the beta phase after the transformation. In this work we present experimental results from in-situ texture measurements performed on the HIPPO neutron diffractometer at LANSCE. Using the combination of time-of-flight neutrons and full-pattern Rietveld analysis allowed us to determine the orientation distribution functions of both phases at room temperature, 800 degrees C, 1020 degrees C and again at room temperature. We found strong indications that the beta phase indeed grows from grains preexisting at room temperature. Upon re-transformation from beta to a we found that the Burgers relationship is followed.