  {\it If} the total number of punctures($N$) of a quantum isolated horizon is
considered to be a macroscopic parameter alongside the Chern-Simons level($k$)
or equivalently classical area$(A_{cl})$ a strict analysis of the {\it
microcanonical} ensemble reveals that the {\it microcanonical} entropy has the
form $S_{MC}=A_{cl}/4\ell_p^2+N\sigma(\gamma)$, only for values of the
Barbero-Immirzi(BI) parameter$(\gamma)$ greater than a certain number. It is
argued that the term $N\sigma(\gamma)$ must be negative definite, which leads
to the bound on the BI parameter.
