Let 22ed3735315f8" title="Click to view the MathML source">(G,⋅) be a finite group of order v. A (G,k,λ) difference matrix (briefly, (G,k,λ)-DM) is a k×λv matrix D=(dij) with entries from G, so that for any distinct rows x and y, the multiset e67c3aa98b820638a517e38fe"> contains each element of G exactly λ times. In this paper, we are concerned about a (G,4,λ)-DM whatever structure of a finite abelian group G is. Eventually for the following two cases: (1) λ=1 and G is non-cyclic, (2) λ>1 is an odd integer, we prove that a (G,4,λ)-DM exists if and only if G has no non-trivial cyclic Sylow 2-subgroups. Moreover, we point out that a (G,4,λ)-DM always exists for any even integer λ≥2 and any finite abelian group G.