This research is a qualitative descriptive study that aims to describe the ability of mathematical representation of high-ability students to solve non-routine problems based on representation indicators. The subjects of this study were students of class XI-IPA Palopo 1 High School. The steps carried out in this study are (1) Observation, (2) Selection of subjects, (3) Non-routine problems, (4) Interviews, (5) Making conclusions on the results of the study. The instrument of this study was the researchers themselves, with the help of several supporting instruments such as (1) diagnostic tests, (2) interview guidelines, and (3) non-routine mathematical tests. The results obtained from this study are highly capable subjects in completing non-routine questions tend to use alternative methods, think inductively and deductively, create conceptual information networks, describe a concept in the form of algebraic symbols, graphic images, patterns , and equations.