A positive non-decreasing function \(F\) belongs to the class \(\text{O}\Pi^+\) if \(\limsup(t\to\infty)(F(st)- F(t))= M(s)\) is finite for every \(s> 1\). Given a non-decreasing slowly varying function \(L\), if, whenever it is written as a sum \(L= F+G\) of two non-decreasing functions, both \(F\) and \(G\) are slowly varying, \(L\) is said to have the good decomposition property in the class of non-decreasing functions. In Theorem 1 the authors prove that \(L\) has this property if and only if it belongs to the class \(\text{O}\Pi^+\). Generalization of this class is also discussed, as is the influence of convexity/concavity.