Development of carbon fibers from alternative precursory materials through new production processes is a recent topic of active research. In such a research, the maximum available tensile strength, i. e. the tensile strength which will be achieved after elaboration to suppress defect formation during production process, is the matter of great concern. We have developed a method for determining this strength through the tensile test on a single fiber after introducing an artificial notch. In the present paper, this method has been refined. By using the refined method, the distribution of the maximum available tensile strength at various radial positions has been measured for a polyacrylonitrile-based carbon fiber. The difference between the maximum available tensile strength and the strength predicted using other methods such as those based on the fracture toughness and the fiber-length dependence of the tensile strength has also been discussed.