This paper presents a new orthogonal neural network (ONN) which is utilized successively for online identification and control of nonlinear discrete-time systems. The proposed network is designed with auto regressive with exogenous (ARX) terms of inputs and outputs, and their orthogonal terms by Chebyshev polynomials. The network is a single layer neural network and computationally efficient with less number of parameters. The identification by the network is performed in stable sense by using Lyapunov stability guaranteed learning rate. Hence, the learning rate depends on the current knowledge of the system instead of using constant learning rate. This learning rate provides fine online optimization. In simulation study, one benchmark nonlinear system is identified and results are compared. Then, one nonlinear functioned system is identified and controlled by model reference control. From results, it is seen that the proposed model has good learning capability for identification and control.