  We present a new multiparticle model of $\mathcal{N}{=}\,8$ mechanics with
superconformal $F(4)$ symmetry. The system is constructed in terms of two
matrix $\mathcal{N}{=}\,4$ multiplets. 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. We demonstrate that the $F(4)$ superalgebra
constructed contains as subalgebras two different $D(2,1;\alpha\,{=}{-}1/3)$
superalgebras intersecting over the common $sl(2,\mathbb{R})\oplus su(2)$
subalgebra.
