A new Ti50Ni48.7Ta1.3 shape memory alloy was designed for medical application. In order to influence the martensitic transformation temperature the alloy was solution treated and additionally aged at 400oC for various time. Phase transformation was studied applying differential scanning calorimeter (DSC) and X-ray diffraction techniques. The ageing causes that the martensitic transformation occurs in two steps: B2↔R↔B19’ during cooling and heating. During cooling the transformations: B2→R and R→B19’ are well separated whereas on heating they are overlapped. Also ageing causes a shift of temperatures of the martensitic transformation into the higher region. It is due to the precipitation process. Precipitates of the Ni4Ti3 phase were observed. Applied thermal treatment leads to shift of the transformation temperatures below temperature of a human body. This makes the Ti-Ni-Ta alloy attractive for application in medicine.