Pseudo-random number series extracted from chaotic and random time series from the chaotic and random neural network (CRNN) with fixed-point arithmetic has been the focus of attention for protecting the information security of IoT devices. Pseudo-random number series generated by a computer is eventually periodic, practically. The produced closed trajectory is not a limit cycle, because which does not divide the phase space into 2 regions. The closed trajectory in this work is called a non-attractive periodic trajectory (NPT) because it hardly attracts trajectories within the neighborhood. The method of preventing the closed trajectory formation has been proposed on the basis of the NPT formation mechanism in this paper. The method has extended the period of NPT considerably. It is expected to apply security applications for IoT devices.