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One of them is a bosonic matrix $({\\bf 1, 4, 3})$ multiplet and another is a fermionic $({\\bf 0, 4, 4})$ one. Off-diagonal bosonic components of the $({\\bf 1, 4, 3})$ multiplet are chosen to take values in the flag manifold $\\mathrm{U}(n)/[\\mathrm{U}(1)]^n$ and they carry additional gauge symmetries. The explicit form of the $F(4)$ supersymmetry generators is found. 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