Let $d\le 3$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. I'm considering an incompressible Newtonian fluid with uniform density $\rho_0$ and viscosity $\nu$. In this case, the stationary Navier-Stokes equations are $$\left\{\begin{matrix}(u\cdot\nabla)u&=&\displaystyle\nu\Delta u-\frac 1\rho_0\nabla p+f&&\text{in }\Omega\\\nabla\cdot u&=&0&&\text{in }\Omega\\u&=&0&&\text{on }\partial\Omega\end{matrix}\right.\;,\tag 1$$ where $f:\Omega\to\mathbb R^d$ is the sum of all external forces.
Assuming $d=1$ for simplicity, the so-called Oseen-iteration is given by $$\left\{\begin{matrix}\displaystyle u^{(n-1)}\frac{du^{(n)}}{dx}&=&\displaystyle\nu\frac{d^2u^{(n)}}{dx^2}-\frac 1\rho_0\frac{dp^{(n)}}{dx}+f^{(n)}&&\text{in }\Omega\\\displaystyle\frac{du^{(n)}}{dx}&=&0&&\text{in }\Omega\\u^{(n)}&=&0&&\text{on }\partial\Omega\end{matrix}\right.\;.\tag 2$$ Using $$\frac{dg}{dx}(x)\approx\frac{g(x+\Delta)-g(x-\Delta)}{2\Delta}\;\;\;\text{and}\;\;\;\frac{d^2g}{dx^2}(x)\approx\frac{g(x+\Delta)-2g(x)+g(x-\Delta)}{\Delta^2}$$ we're left with a system of linear equations: $$\left\{\begin{matrix}\displaystyle u_{k}^{(n-1)}\left(u_{k+1}^{(n)}-_{k-1}^{(n)}\right)&=&\displaystyle\frac{2\nu}\Delta\left(u_{k+1}^{(n)}-2u_{k}^{(n)}+u_{k-1}^{(n)}\right)-\frac 1\rho_0\left(p_{k+1}^{(n)}-p_{k-1}^{(n)}\right)+2\Delta f_k\\\displaystyle\frac{u_{k+1}^{(n)}-u_{k-1}^{(n)}}{2\Delta}&=&0\\u_k^{(n)}&=&0\end{matrix}\right.\;,\tag 3$$ where $x_k=k\Delta$, $g_k:=g(x_k)$ and the equations need to hold for $k$ with $x_k\in\Omega$ or $x_k\in\partial\Omega$, respectively. However, as you may have already observed, the second equation is equivalent to $$u_{k+1}^{(n)}=u_{k-1}^{(n)}\;\;\;\text{for }x_k\in\Omega\;.$$ Thus, the first equation can be simplified to $$0=\frac{4\nu}\Delta\left(u_{k+1}^{(n)}-u_{k}^{(n)}\right)-\frac 1\rho_0\left(p_{k+1}^{(n)}-p_{k-1}^{(n)}\right)+2\Delta f_k\;\;\;\text{for }x_k\in\Omega\;.$$
Hence, the $u_{k}^{(n-1)}$ of the corresponding previous iteration are gone. Did I made any mistake? Since the $u_{k}^{(n-1)}$ are gone, there is no "iteration" anymore.