The dual space of the sequence space bvp (1 ￡ p ￥)

. The sequence space bvp consists of all sequences (xk) such that (xk - xk - 1) belongs to the space lp. The continuous dual of the sequence space bvp has recently been introduced by Akhmedov and Basar [Acta Math. Sin. Eng. Ser., 23(10), 2007, 1757 - 1768]. In this paper we show a counterexample for case p = 1 and introduce a new sequence space d￥ instead of d1 and show that bv1* = d￥. Also we have modified the proof for case p > 1. Our notations improves the presentation and confirms with last notations l1* = l￥ and l1* = lq.