Recently Hong and Oh [5] provided a fairly general weak law for arrays in the following form: Let {(X_ni, l ≤ i ≤ k_n), n ≥ l}, k_n → ∞ as n → ∞, be an array of random variables on (Ω, F, P) and set F_nj = σ{X_ni, 1 ≤ i ≤ j}, 1 ≤ j ≤ k_n, n ≥ 1, and F_n0 = {ø, Ω}, n ≥ 1. Suppose that (equation omitted) aP { X_ni ^p ＞ a} → 0 as a → ∞ uniformly in n for some 0 < p < 2. Then S_n/(equation omitted) → 0 in probability as n → ∞ where S_n = (equation omitted)(X_ni - E(X/sib ni/I( X_{ni p} ≤ k_n) F_n,i-l)). In this note, we will prove the following result under the same domination condition of Hong and Oh [5].(omitted)