Abstract: For the seemingly unrelated regression system, 1 proposes a new estimate of regression coefficients, called the covariance-improved estimate （OIE）. This paper compares the estimate and its two-stage version （TCIE） with the singuly equation least-squares estimate （LSE） in term of computer simulation. The results show the efficiency of the OIE and TCIE with respect to the LSE. For the models used in the paper the two estimates have the priority over the LSE when there is considerable correlation among the error terms of the equations, e. g. ρ_ij≥0.3, or the sample size is not too small, e. g. n≥25.