The martensitic phase transition in Ni₂MnGa, fundamental to its shape memory behaviour, can be described by two successive 110 type shears leading to 36 possible different orientations for the axes of the pseudo-tetragonal martensitic phase. The distribution and orientation of the domains formed on cooling Ni₂MnGa into the martensitic phase has been studied using single-crystal neutron diffraction with a multi-detector. The number of domains actually occurring was rather low and was reduced by residual strain. Thermal cycling through the phase transition was found to further reduce the number of domains occurring, which may stabilize after several cycles. Uniaxial stress or a magnetic field applied parallel to [001] is able to switch domains whose pseudo-tetragonal axis is [100] or [010] to ones of type [001]. The results suggest that plastic deformation in the martensitic phase takes place by twinning (change of domain), rather than by slip and that the shape memory property arises from the fixed orientation relationship between the martensitic twins and the high temperature cubic axes.