  We report the results of a BeppoSAX observation of the composite supernova
remnant G0.9+0.1, located in the Galactic Center region. This new observation,
in which the core of G0.9+0.1 is observed on-axis, confirms our previous
results obtained from a pointing in which the supernova remnant was
serendipitously observed at a large off-axis angle. The better quality of the
new data allows us to confirm the non-thermal nature of the X-ray source
coincident with the central plerion, to significantly improve the estimate of
its spectral parameters, to put more stringent upper limits on the presence of
coherent pulsations (in the range of periods from 4ms to ~ 4\times10^4 s), to
obtain marginal evidence of the possible extended nature of the X-ray plerion
and to put a better upper limit on the 2--10 keV X-ray emission from the 8'
diameter radio shell (L$_{\rm S}<3.4\times 10^{34} {\rm d}_{10}^{2}$ erg
s^{-1}). The X-ray spectrum is best fit with a power-law model with a photon
index \Gamma ~ 2, N_{\rm H} ~ 10^{23} \hcm and a 2-10 keV luminosity of
7.5\times 10^{34} {\rm d}_{10}^{2} erg s^{-1}. The broad band (radio-X-ray)
properties of the composite supernova remnant G0.9+0.1 are indicative of the
likely presence of a young (~ 2,700 yr) neutron star in its central radio core.
