It is well known that two mutually related summability methods for a sequence sn(n = 0, 1, 2, …) are any Cesaro method (C, γ) of order γ > 0 and the Abel method (A). The notation used in this statement is that of Hardy ((1), pp. 96-7, 71) and the statement itself can be amplified as follows. Summability (C, γ), γ > 0, of sn implies (i) sn = o(nγ), (ii) summability (A) of sn. Also, as a conditional converse of this result, we have Offord's result ((3), first part of Theorem 2), that hypothesis (i), and hypothesis (ii) suitably strengthened, together imply summability (C, γ), γ > 0, of sn. It is the object of this note to bring to light a second pair of summability methods mutually related like the methods (C, γ) and (A), by following an argument which is essentially similar to Offord's but differs sufficiently from Offord's in details to justify a separate and self-contained treatment of the second pair of methods.