We show that if a graph \(G\) on \(n\) edges allows certain special type of rosy labeling (a.k.a. \(\rho\)-labeling), called \(\alpha_2\)-labeling, then for any positive integer \(k\) the complete graph \(K_{2nk+1}\) can be decomposed into copies of \(G\). This notion generalizes the \(\alpha\)-labeling introduced in 1967 by A. Rosa.