By the decomposition theorem and the Ljapunov function \(V^{(i)}=| X^{(i)}|\), the stability of the zero solution of an iteration system with variable coefficients is considered. If the linear iteration system \(X(\tau +1)=P(\tau)X(\tau)\) has the decomposition \(X^{(i)}(\tau +1)=P_{ii}(\tau)X^{(i)}(\tau)+\sum^{r}_{i=1,j\neq i}P_{ij}(\tau)X^{(j)}(\tau),\) where \(X^{(i)}\in R^{n_ i}\), \(\sum^{r}_{i=1}n_ i=n\), \(P_{ii}(\tau)\) is an \(n_ i\times n_ i\) matrix for \(i\in I=\{1,2,...,r\}\), the authors prove that the solution of the system is stable under the conditions of \(\| P_{ii}(\tau)\| <1\) and \(\epsilon <A/2(r-1)\), where \(\epsilon =\max_{i\neq j,i,j\in I}\{\| P_{ij}(\tau)\| \}\) and \(A=\min_{i\in I}\{(1-\| P_{ii}(\tau)\|)\}.\)