Let \(S\) be a totally disconnected compact Hausdorff space and \(C(S)\) be the usual Banach space consisting of all continuous real-valued functions on \(S\). Then it is known that the closed unit ball \(U\) in \(C(S)\) is not compact but is still the closed convex hull of its extreme points. The paper under review gives a short proof of the stronger property that \(U\) is the sequentially-convex hull of its extreme points.