Traditional Item relational structure theory can only be used to detect the item relational structure for a group of subjects, but not for individuals. In this paper, an extensional item relational structure theory based on Liu's new improved nonparametric item response theory is proposed. It can be used to detect the item relational structure for not only a group of subjects, but also each individual. This new method may provide more information for planning remedial instruction, developing instruction materials, or educational researches than before. A mathematics example is also provided in this paper to illustrate the advantages of the proposed method.