  We give a complete characterization of all indecomposable involutive
solutions of the Yang-Baxter equation of multipermutation level~2. In the first
step we present a construction of some family of such solutions and in the
second step we prove that every indecomposable involutive solution of the
Yang-Baxter equation with multipermutation level~2 is a homomorphic image of a
solution previously constructed. Analyzing this epimorphism, we are able to
obtain all such solutions up to isomorphism and enumerate these of small sizes.
