**MSC:**- 46E10 Topological linear spaces of continuous, differentiable or analytic functions

This work considers DFS-spaces\footnote[2]{An inductive limit of F spaces

with compact embedding operator.} of ultradifferentiable functions on interval.

Unlike the results of R.Meise's and A.Taylor's works [8,9], we give a method

for concretely construction of continuous linear extension operator.

We also considered the relations between a basis and a continuous

linear extension operator of the functions outside an interval.