Neutron diffraction was applied to investigate the martensitic transformation of an off-stoichiometric Heusler-type Ni2.16Mn0.78Ga1.06 single crystal (conduction electron-to-atom ratio = 7.56). The splitting of a cubic (020) peak on a reciprocal lattice c*-plane was traced with decreasing temperature from 400 to 37 K. It was found that an orthorhombic structure (a > b > c) appears slightly below the transformation temperature as a metastable transient precursor structure before the formation of a final stable tetragonal structure (a = b < c). The modes of deformation from cubic to orthorhombic are (i) simple shrinking and elongation of two cubic axes or (ii) a shuffling-like deformation along the cubic < 110 > direction on one of the cubic planes. The mode of deformation from orthorhombic to tetragonal is a shuffling-like deformation along the orthorhombic < 110 > direction on the orthorhombic c-plane. Both shuffling-like deformations originate from tilting deformations that preserve the common < 111 > direction.