  Let $\mathbb{k}$ be an algebraically closed field. We give a complete
classification of non-connected pointed Hopf algebras of dimension $16$ with
char$\,\mathbb{k}=2$ that are generated by group-like elements and
skew-primitive elements. It turns out that there are infinitely many classes
(up to isomorphism) of pointed Hopf algebras of dimension 16. In particular, we
obtain infinitely many new examples of non-commutative non-cocommutative
finite-dimensional pointed Hopf algebras.
