Let $W\subset U\subset V$ where $W,U$ are compact strictly $K$-analytic domains of $V$ with $W\subset U^{\circ}$. Let $f\colon W\to{\mathbb{R}}$ be a piecewise linear function. Then $f$ extends to a piecewise linear function $\varphi\colon V\to{\mathbb{R}}$ such that ${\rm supp}(\varphi)\subset U$.