Bounded Component Analysis (BCA) solves the Blind Source Separation (BSS) problem based on geometric assumptions. This paper introduces a new proof of a BCA contrast function, derived from elementary matrices, Gauss–Jordan elimination and convex geometry. The new proof and further analysis provide additional insight into a key assumption of BCA. In addition, an interpretation is presented to clarify one of the limitations of the instantaneous BCA algorithm. Experiments on audio sources support our analysis.