A training rule for neural network controllers that guarantees finite-region stability of control systems has recently developed. The training rule requires that the controlled systems must be locally hermitian, controllable, and full state accessible. The controller is a single hidden layer feedforward networks. This present paper extends the training rule by modifying the stability condition to drop out the hermitian requirement. A finite stability region is estimated by evaluating an existing Lyapunov function, which is a by-product of the training rule.