  The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg
antiferromagnetic chain with alternating couplings AF$_{1}$-AF$_{2}$-AF$_{1}$%
-F (AF and F denote antiferromagnetic and ferromagnetic couplings,
respectively) are studied by means of the density matrix renormalization group
method. Two plateaux of magnetization $m$ are found at $m=0$ and 1/4% . It is
shown that in such a spin-1/2 AF system, there is a gap from the singlet ground
state to the triplet excited states in the absence of a magnetic field. The
spin-spin correlation function decays exponentially, and the gapped states have
a nonvanishing string order, which measures a hidden symmetry in the system. By
a dual transformation, the string order is transformed into a ferromagnetic
order and the hidden symmetry is unveiled to be a $Z_{2}\times Z_{2}$ discrete
symmetry, which is fully broken in the gapped states. This half-integer spin
Heisenberg AF chain is in a Haldane-like phase, suggesting that the present
findings extend the substance of Haldane's scenario. A valence-bond-solid state
picture is also proposed for the gapped states.
