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 4 ms to \sim 4 \times 10 ^ { 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 ^ { \prime } diameter radio shell ( L _ { S } < 3.4 \times 10 ^ { 34 } ~ { } { d } _ { 10 } ^ { 2 } erg s ^ { -1 } ) . The X–ray spectrum is best fit with a power–law model with a photon index \Gamma \sim 2 , N _ { H } \sim 10 ^ { 23 } cm ^ { -2 } and a 2–10 keV luminosity of 7.5 \times 10 ^ { 34 } ~ { } { 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 ( \sim 2,700 yr ) neutron star in its central radio core .