As well-known, the preceding result is a generalization of Krein's theorem (see [1, p. 218]) to the ease of ordered locally convex spaces. Unfortunately his proof, as given El, p. 219] is based on Krein's theorem. In this note we give another proof which avoids Krein's result. Before proving this result, we require the following terminology and recall some well-known facts. Let (E, Z) be a locally convex space with a positive cone C. A subset A of E is said to be C-saturated if A = ( A + C ) c ~ ( A C ) . C is said to be normal with respect to ~ if ~ admits a neighbourhood-base of 0 consisting of C-saturated, convex, and circled sets in E. C' is called a strict C-cone if the family {A n C' A n C' : A e C} is a fundamental subfamily of C (for definition see [1, p. 79]). If W is an absorbing subset of E, Pw denotes always the gauge of W, co(W) (resp. F(W)) denotes the convex hull (resp. convex, circled hull) of IV, and W ° denotes the polar of W in E'; namely W ° = { f ~ E' : f (x) < 1 for all x in W}. Let W and U be convex ~-neighbourhoods of 0. According to the Hahn-Banach theorem, we have