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Magnetic properties of Ni46.0Mn36.8Sn11.4Co5.8/MgO(001) epitaxial thin film, which undergo a martensitic phase transformation from cubic austenitic phase to a twinned orthorhombic martensitic phase at 270 K, were studied by the magnetic resonance at the microwave frequency of 9.45 GHz. It was found that the single resonance line observed in the austenite splits into three lines in the martensitic phase. A theoretical approach was developed to show that the additional resonance lines are caused by the weak antiferromagnetic coupling of the ferromagnetic twin components across twin boundaries. Fitting of the experimental resonance lines to model gives an effective field of antiferromagnetic coupling of about 1.5 kOe, which is two or three orders of magnitude lower than in the conventional antiferromagnetic solids because the number of magnetic ions interacting antiferromagnetically through the twin boundary is much less than the total number of magnetic ions in the twin. This feature shows a strong resemblance between the submicron twinned martensite and artificial antiferromagnetic superlattices, whereby providing a distinctive insight into magnetism of the studied magnetic shape memory material.