A partition \(\mathcal{D} = \{V_1, \ldots, V_m\}\) of the vertex set \(V(G)\) of a graph \(G\) is said to be a star decomposition if each \(V_i\) (\(1 \leq i \leq m\)) induces a star of order at least two.
In this note, we prove that a connected graph \(G\) has a star decomposition if and only if \(G\) has a block which is not a complete graph of odd order.