The purpose of this note is to characterize those Banach lattices (E, ∥·∥) which have the property:an operator T: E → c0 is a Dunford-Pettis operator if and only if T is regular (*)(i.e., T is the difference of two positive operators). Our characterization generalizes a theorem recently proved by Holub [6] and Gretsky and Ostroy [4], who have remarked that the space L1[0, 1] has the property (*). The main result presented here is the following theorem.