  The level spacing distribution is numerically calculated at the
disorder-induced metal--insulator transition for dimensionality d=4 by applying
the Lanczos diagonalisation. The critical level statistics are shown to deviate
stronger from the result of the random matrix theory compared to those of d=3
and to become closer to the Poisson limit of uncorrelated spectra. Using the
finite size scaling analysis for the probability distribution Q_n(E) of having
n levels in a given energy interval E we find the critical disorder W_c = 34.5
\pm 0.5, the correlation length exponent \nu = 1.1 \pm 0.2 and the critical
spectral compressibility k_c \approx 0.5.
