  For two positive maps $\phi_i:B(\mathcal{K}_i)\to B(\mathcal{H}_i)$, $i=1,2$,
we construct a new linear map $\phi:B(\mathcal{H})\to B(\mathcal{K})$, where
$\mathcal{K}=\mathcal{K}_1\oplus\mathcal{K}_2\oplus\mathbb{C}$,
$\mathcal{H}=\mathcal{H}_1\oplus\mathcal{H}_2\oplus\mathbb{C}$, by means of
some additional ingredients such as operators and functionals. We call it a
merging of maps $\phi_1$ and $\phi_2$. We discuss properties of this
construction. In particular, we provide conditions for positivity of $\phi$, as
well as for $2$-positivity, complete positivity and nondecomposability. In
particular, we show that for a pair composed of $2$-positive and $2$-copositive
maps, there is a nondecomposable merging of them. One of our main results
asserts, that for a canonical merging of a pair composed of completely positive
and completely copositive extremal maps, their canonical merging is an exposed
positive map. This result provides a wide class of new examples of exposed
positive maps. As an application, new examples of entangled PPT states are
described.
