School climate is a relevant construct for understanding social relations at school. The SCASIM-St has been widely defined as a multidimensional construct; however, new factor structures have not been explored through evidence that allows for interpreting school climate scores from an approach that respects the multidimensionality of the scale and, at the same time, allows for identifying the degree of essential unidimensionality in the data. Consequently, the objective was to analyze the psychometric properties of the SCASIM-St from a bifactor model approach, evaluating the influence of a general school climate factor versus five specific factors. The study involved 1860 students of both sexes (42% males and 58% females), with an average age of 16.63 years (SD = 0.664), from 17 secondary schools in Chile. The results obtained by a confirmatory factor analysis provided evidence that the best model was the bifactor model for the 38 items, with one general factor and five specific factors. The Explained Common Variance (ECV) values and reliability levels by hierarchical omega accounted for a strong general school climate factor with high levels of reliability. Evidence of external criterion validity, assessed through the attitude toward authority scale (AIA-A), showed a theoretically expected and significant relationship between the factors of both instruments. This study confirmed the psychometric robustness of the SCASIM-St scale by means of a bifactor model, allowing for a new, essentially unidimensional interpretation of the scale scores and providing an instrument to measure school climate in Chile.