  We generalize in this work the properties of the conjugacy of skew tent maps.
It is known that the conjugacy $h$ from a skew tent map $g_1$ to $g_2$ is
differentiable at a point $x^*$ if and only if there exists left and right
limits $\lim\limits_{n\rightarrow \infty}h_n'(x^*-)$ and
$\lim\limits_{n\rightarrow \infty}h_n'(x^*+)$, where $h_n$ is a piecewise
linear function, which coincides with $h$ at $g_1^{-n}(0)$, and all whose kinks
belong to $g_1^{-n}(0)$. The attempts to generalize this result to some reacher
class of unimodal maps is natural. For this reason we introduce the class of
piecewise linear maps, all whose kinks are in the complete pre-image of $0$ and
study the relation of the differential properties of their conjugacy with ones
of the mentioned approximation~$(h_n)_{n\geq 1}$.
