According to well-known theorems of Kaplansky and Baer–Kulikov–Kapla nsky–Fuchs (4, 2), the class of direct sums of countable Abelian groups and the class of direct sums of torsion-free Abelian groups of rank 1 are both closed under the formation of direct summands. In this note I give an example to show that the class of direct sums of torsion-free Abelian groups of finite rank does not share this closure property: more precisely, there exists a torsion-free Abelian group G which can be written both as a direct sum G = A⊕B of 2 indecomposable groups A, B of rank ℵ0 and as a direct sum G = ⊕n ε zCn of ℵ0 indecomposable groups Cn (nεZ) of rank 2, where Z is the set of all integers.