  For a dynamical map $\Lambda(t,0)$, which sends a state $\rho(0)$ of quantum
open system to a state $\rho(t)=\Lambda(t,0)\rho(0)$, the decomposition law
$\Lambda(t,0)=\Lambda(t,t_c)\Lambda(t_c,0)$ may break down at a specific time
$t_c$. In this paper, we present a method to find the singular points $t_c$ and
propose a measure for the singularity of the dynamical map. Two examples are
portrayed to illustrate the method, the measure of singularity for these
singular points is calculated and discussed. An extension to high-dimensional
system is presented.
