By the aid of the linear quantum transformation (LQT) theory,we give a concise diagonalization for n-mode boson and fermion of quadratic Hamiltonian. It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).