[en] The magnetic controllability of the thermoelastic martensitic transformation, which is the origin of the shape-memory effect, has been investigated. We have carried out neutron diffraction measurements of a Heusler-type off-stoichiometric Ni_2.19 Mn_0.81Ga alloy under the magnetic field of up to 5T using the HERMES and the TAS-2 diffractometers both installed at the JRR-3M reactor of Japan Atomic Energy Research Institute (JAERI). This alloy has the martensitic transformation temperature (M_s point) of about 350K, which coincides with the magnetic Curie temperature )T_c). It is ferromagnetic in the martensitic phase and paramagnetic in the cubic Heusler phase. By Rietveld analysis of the diffraction patterns we have confirmed that the martensitic phase and the cubic phase coexist at 350K. We have also discovered that half of the cubic phase changes to martensitic phase under the magnetic field of 5T at this temperature. This finding indicates the possibility of controlling the martensitic transformation by means of the external magnetic field. (author)