Let
u
1
,
…
,
u
n
{u_1}, \ldots ,{u_n}
be linearly independent continuously differentiable functions on the unit interval. In this paper, we obtain the following two results. One is a necessary and sufficient condition for the span of
{
1
,
u
1
,
…
,
u
n
}
\{ 1,{u_1}, \ldots ,{u_n}\}
to have a Markoff basis containing 1. The other is that any Markoff system
{
u
i
}
i
=
1
n
\{ {u_i}\} _{i = 1}^n
has a Tchebysheff extension
u
n
+
1
{u_{n + 1}}
which is continuously differentiable.