[en] It has previously been shown that if G a subset of Csup(n) is a strongly pseudoconvex domain, then to every boundary point P an element of delta G there exists a function f(z) holomorphic in a neighbourhood of G-bar (the closure of G) such that |f(z)| assumes its maximum in G-bar at P and only at P. Now the following theorem is proved. Let G be a strongly pseudoconvex domain in Csup(n) and P, Q be elements of delta G, P not equal to Q. Then there exists a function f(z) holomorphic in a neighbourhood of G-bar, such that |f(P)|=|f(Q)|=Max|f(anti G)|=1, f(P) not equal to f(Q) and |f(T)|<1, for all T elements of G-bar - set (P,Q). This theorem is used to improve the results already obtained by the author concerning the Caratheodory metric and the Caratheodory limiting balls in G. Similar results do not exist if G is only pseudoconvex