Summary: Let \(R\) be a ring and \(M\) a left \(R\)-module. Then, \(M\) is called a \((D_{11})\)-module if every submodule of \(M\) has a supplement that is a direct summand of \(M\), and \(M\) is called a \((D^{+}_{11})\)-module if every direct summand of \(M\) is a \((D_{11})\)-module. In this paper, the author characterizes the \((D^{+}_{11})\)-module \(N\in\delta[M]\) in terms of \(\overline Z^2_M(N)\).