We study spectral statistics of a Gaussian unitary critical ensemble of
almost diagonal Hermitian random matrices with off-diagonal entries
$<|H_{ij}|^{2} > \sim b^{2} |i-j|^{-2}$ small compared to diagonal ones
$<|H_{ii}|^{2} > \sim 1$. Using the recently suggested method of {\it virial
expansion} in the number of interacting energy levels (J.Phys.A {\bf 36},8265
(2003)), we calculate a coefficient $\propto b^{2}\ll 1$ in the level
compressibility $\chi(b)$. We demonstrate that only the leading terms in
$\chi(b)$ coincide for this model and for an exactly solvable model suggested
by Moshe, Neuberger and Shapiro (Phys.Rev.Lett. {\bf 73}, 1497 (1994)), the
sub-leading terms $\sim b^{2}$ being different. Numerical data confirms our
analytical calculation.