Let $Ax=b$ for $A \in \mathbb{C}^{n \times n}$ and $b \in \mathbb{C}^n$ be a linear system and $x^{(0)},~x^{(k+1)}=Tx^{(k)}+d$ be one of Jacobi's or Gauss-Seidel's iteration formula for solving the linear system. In this work, we introduce some bounds on the departure from normality of the iteration matrices $T$ for some special coefficient matrices $A$.
