Martensitic transformations are of considerable technological importance, a particularly promising application being the possibility of using martensitic materials, possibly proteins, as tiny machines. For organic crystals, however, a molecular level understanding of such transformations is lacking. We have studied a martensitic-type transformation in crystals of the amino acid DL-norleucine using molecular dynamics simulation. The crystal structures of DL-norleucine comprise stacks of bilayers (formed as a result of strong hydrogen bonding) that translate relative to each other on transformation. The simulations reveal that the transformation occurs by concerted molecular displacements involving entire bilayers rather than on a molecule-by-molecule basis. These observations can be rationalized on the basis that at sufficiently high excess temperatures, the free energy barriers to concerted molecular displacements can be overcome by the available thermal energy. Furthermore, in displacive transformations, the molecular displacements can occur by the propagation of a displacement wave (akin to a kink in a carpet), which requires the molecules to overcome only a local barrier. Concerted molecular displacements are therefore considered to be a significant feature of all displacive transformations. This finding is expected to be of value toward developing strategies for controlling or modulating martensitic-type transformations.