In a recent paper, [Sarigöl, M. A.: Characterization of summability methods with high indices, Math. Slovaca 63 (2013), 1053–1058], the equivalence ∣C, 0∣
k
⟺ ∣R, pn
∣
k
, k ≥ 1, was characterized for infinite single series. In the present paper, this result is extended to doubly summability a different approach.