This paper considers a system of two seemingly unrelated equations. Without imposing any additional restrictions on the matrices of observations on the independent variables in the two equations, we derive the exact second moments of Zellner's estimator [9]. Though not uniformly more efficient than the corresponding single-equation least-squares estimator, a definite efficiency gain results using Zellner's estimator in the presence of high contemporaneous correlation coefficient (ρ) between the disturbances in the two equations, and little loss results when the true ρ is small and the excess of the sample size over the number of distinct regressors in this system is greater than 12.