  The dynamic susceptibility $\chi_{Q}^{zz}(\omega)$ of the isotropic XY-model
(s=1/2) on the alternating superlattice (closed chain) in a transverse field
$h$ is obtained exactly at arbitrary temperatures. It is determined from the
results obtained for the dynamic correlations $<S_{jn}^{z}(t)S_{lm}^{z}(0)>$,
which have been calculated by introducing the generalized Jordan-Wigner
transformation, by using Wick's theorem and by reducing the problem to a
diagonalization of a finite matrix. The static properties are also reobtained
within this new formalism and all exact results are determined for arbitrary
temperatures. Explicit results are obtained numerically in the limit T=0, where
the critical behaviour occurs. A detailed analysis is presented for the
behaviour of the static susceptibility $\chi_{Q}^{zz}(0)$, as a function of the
transverse field h, and for the frequency dependency of the dynamic
susceptibility $\chi_{Q}^{zz}(\omega)$. It is also shown, in this temperature
limit, that within the magnetization plateaus which correspond to the different
phases, even when the induced magnetization is not saturated, the effective
dynamic correlation, $<\sum\limits_{n;m\in
cell:\text{}j;l}S_{jn}^{z}(t)S_{lm}^{z}(0)>$, is time independent, which
constitutes an unexpected result.
