Let $[a,b]$ be a nondegenerate compact interval, let $V \subset C[a,b]$ be an $n$-dimensional Haar space, and let $f \in C[a,b]$. If $h \in V$ is a best uniform approximant to $f$ and $f-h$ is not identically zero, then the residual $r=f-h$ attains its uniform norm at points \begin{align*} a \le t_0 < t_1 < \cdots < t_n \le b \end{align*} with alternating signs: \begin{align*} r(t_i)=\sigma(-1)^i\|r\|_\infty, \quad i=0,\dots,n, \end{align*} for some $\sigma \in \{-1,1\}$. If $f \in V$, then the unique best approximant is $h=f$ and the residual is zero.