We say that a simple graph $G$ is Seidel integral if its Seidel spectrum consists entirely of integers. If $\alpha K_{a,a}\cup \beta K_{b,b}$ is Seidel integral, we show that it belongs the class of Seidel integral graphs \[ \Big[\frac{kt}{au}x_0 + \frac{mt}{au}z\Big]K_{a,a}\cup \Big[\frac{kt}{au}y_0 + \frac{a}{au}z\Big]nK_{b,b}, \] where (i) $a = (t + \ell n)k + \ell m$ and $b = \ell m$; (ii) $t,k,\ell,m,n\in \mathbb N$ such that $(m,n) = 1$, $(n,t) = 1$ and $(\ell,t) = 1$; (iii) $\tau = (a,mt)$ such that $\tau\mid kt$; (iv) $(x_0,y_0)$ is a particular solution of the linear Diophantine equation $ax - (mt)y = \tau$ and $(v)$ $z\geq z_0$ where $z_0$ is the least integer such that $\big(\frac{kt}{\tau}x_0 + \frac{mt}{\tau}z_0\big)\geq 1$ and $\big(\frac{kt}{\tau}y_0 + \frac{a}{\tau}z_0\big)\geq 1$. In particular, we demonstrate that $\overline{\alpha K_a\cup \beta K_b}$ is integral in respect to its ordinary adjacency matrix if and only if $\alpha K_{a,a}\cup \beta K_{b,b}$ is Seidel integral.