Abstract: Homogenized Ni39.6Mn47.5T12.9 material was investigated by different electron microscopy techniques. Apart from the martensite precursor distortions typical for B2 phase alloys undergoing a thermoelastic martensitic transformation upon cooling, coherent dodecahedron-shaped precipitates with sizes between 20 and 100 nm and faceted by lozenge shapes of {110}-type planes are observed. Selected-area and microdiffraction patterns reveal an overall unit cell with a size of 3 x 3 x 3 units of the bcc lattice of the matrix and a body-centred symmetry without screw axes. Finally a ternary gamma-brass-type atomic structure of space group 14(3) over bar m is suggested for these precipitates in accordance with the obtained symmetry constraints, the energy-dispersive X-ray measurements and high-resolution transmission electron microscopy images. This is the first time this type of structure is found in an alloy completely consisting of transition-metal elements.