If a matroid M satisfies (M) n,but for any e E(M), (M e) < n, then M is a minimally n-connected matroid. Let r(M) = r 2. Then each of the following holds. (i) If n r, then |E(M)| r + n 1, where equality holds if and only if M isomorphic to Ur,r+n1.

(ii) If n > r, then |E(M)| 2r 1, where equality holds if and only if M isomorhic toUr,2r1.