Let $Av = b$ be an overdetermined system of m complex equations in n unknowns with rank $(A) = k$ and $m \geqq 2k + 1$. It is shown that if $x_\infty $ is a Chebyshev solution of $Av = b$, then $x_\infty $ is also a Chebyshev solution of a $2k + 1 \times n$ subsystem of $Av = b,A_{2k + 1} v = b_{2k + 1} $. Furthermore, $\| {b - Ax_\infty } \|_\infty = \| {b_{2k + 1} - A_{2k + 1} x_\infty } \|_\infty $.Finally if $(\| \cdot \|_n )$ is a sequence of norms with the property that for each a in $C^n ,\| a \|_\infty \leqq \| a \|_n $ and $\lim _{n \to \infty } \| a \|_n = \| a \|_\infty $, it is shown that a sequence of best $\| \cdot \|_n $-approximate solutions of the overdetermined system of equations $Av = b$ converges to a best $\| \cdot \|_\infty $-approximate solution called the strict approximation.