We propose an improved supervisory training rule for multilayered feedforward neural networks (FNNs). The proposed method analytically estimates the optimal solutions for the output weights of FNNs. Also, using the optimal solutions, it reduces the searching space as much as the output weights in the iterative high-dimensional nonlinear optimization problem for the supervisory training. As a result, we can secure a much faster convergence rate and better robustness compared to the previous full-dimensional training rules.