Given a unital C *-algebra A, let M m×n (A) be the set of all m×n matrices algebra over A and M n (A) 1 be the closed unit ball of M n×n (A). Let x = a b 0 c ∈ M m+n (A) 1 be determined by a ∈ M m×m (A), b ∈ M m×n (A) and c ∈ M n×n (A). Some characterizations are given such that the above upper triangular matrix x is an extreme point of M m+n (A) 1 and X m,n (A) respectively, where X m,n (A) is the subset of M m+n (A) 1 consisting of all upper triangular matrices.