Summary: Let \(A\) be a quasi-injective right \(R\)-module. It is shown that for any \(R\)-monomorphisms \(f,g\colon M\to A\), there exist a split \(R\)-epimorphism \(h_1\in\text{End}_R(A)\) and a split \(R\)-monomorphism \(h_2\in\text{End}_R(A)\) such that \(h_1h_2g=f\). The dual is also obtained.