In order to solve the problem why it was hard to observe the single-variable nonlinear system, this article proposed the 45 line method. In this method, the continuous signal changing with time was transformed into dots on the 45 line of the rectangular coordinates, so that it could be directly displayed on a general dual-trace oscilloscope (either analog or digital). In this way, it is convenient to directly observe and analyze various states of single-variable system while the system is running, such as the periodical stable states, the local and global non-stable states. The mechanism of this method was expounded in this paper. In addition, the key issues in physical circuit design and implementation of this method were researched and solved, i.e., the useful signal which reflected the state of the system could be extracted from the continuously changing signal. Since the Chuas circuit is a typical nonlinear system, and it could produce abundant states with variation of parameters, so it was chosen as the system under test to conduct a great number of physical experiments. The experimental results confirmed the effectiveness and practicability of this method.