We study the finite sample properties of an asymptotically efficient estimator for coefficients of seemingly unrelated unrestricted regression (SUUR) equations. Zellner (1963) derived the exact probability density function of the SUUR estimator. The new form of the probability density function, the r th moment, the characteristic function and the asymptotic expansion distribution of SUUR equations up to order n^-r are derived by Youssef, A. (1996). Youssef. et. al. (1995) studied the statistical curvature for SUUR estimator up to order n^-1. In this paper, we study the statistical curvature for SUUR estimator when the asymptotic expansion distribution of SUUR equations is of order n^-2, because it is hard to deal with order higher than two, to examine how close the density function of Zellner's estimator is to the normal distribution.