Abstract: The strengthening forms of Janic＇'s R R type inequalities on the high dimensional simplex are given: １≤ｉ＜ｊ≤ｎ＋１ａ２ｉｊ／(ｒｉｒｊ)≥ｎ２（ｎ－１）２（Ｒ／(ｎｒ)）２／(ｎ（ｎ－１）)≥ｎ２（ｎ－１）２，and the sufficient and necessary condition for the equalities is that Ω　is canonical simplex.

Key words: Janic＇&rsquo, s inequality；high dimensional simplex；strengthening form