In this note, the norm bounds and convex properties of special operator matrices H (m) n and S (m) n are investigated. When Hilbert space K is infinite dimensional, we firstly show that H (m) n = H (m) n+1 and S (m) n = S (m) n+1 , for m, n = 1, 2, · · ·. Then we get that H (m) n is a convex and compact set in the ω * topology. Moreover, some norm bounds for H (m) n and S (m) n are given.