This note is about another relation between the Horn conjecture and the sequences of stretched Littlewood-Richardson coefficients. In Section 2, the author gives an idea of the history of the proof and the subjects interplaying with it. Section 3 is concern with the codimension one faces of the Horn cones. Sections 2 and 3 are mainly expository. The last section is the author’s proof of Fulton’s conjecture.