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A giant four-fold magnetic anisotropy (with an anisotropy field up to 4 kOe) was observed in the twinned NiMnGa epitaxial film. Its appearance is explained in terms of moderate coupling between twin variants having strong uniaxial magnetocrystalline anisotropies directed orthogonally when the intertwin exchange field is comparable with the anisotropy field. This finding paves the way to increase the order of magnetic anisotropy in a many-component system while keeping the value of the anisotropy field by tuning the intercomponent exchange strength and can be extended to exchange-coupled multilayers and arrays of nanoelements.