The random variable $\varsigma$ is called a composed random variable of two random variables $\xi$ and $\eta$ if its characteristic function has the form $$\psi(t)=a[\phi(t)]$$ where $a[z]$ is the generating function of $\eta$ and $\phi(t)$ is the characteristic function of $\xi$. In our previous papers, we have considered a stability condition for characteristic functions of a class of composed random variables. In this paper, we consider another condition for the characteristic function of the composed random variable of $\xi$ and $\eta$, if $\eta$ is also a composed random variable.