  We obtain the phase diagram in the parameter space $(J'/J, \gamma)$ and an
accurate estimate of the critical line separating the different phases. We show
several measuments of the magnetization, dimerization, nearest neighbours
correlation, and density of energy in the different zones of the phase diagram,
as well as a measurement of the string order parameter proposed as the non
vanishing phase order parameter characterizing Haldane phases. All these
results will be compared in the limit $J'/J\gg 1$ with the behaviour of the
$\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of our
data supports the existence of a dimer phase separated by a critical line from
a Haldane one, which has exactly the same nature as the Haldane phase in the
$\textbf{S}=1$ BAHC.
