  In this paper we give a complete classification of the Leibniz algebras of
biderivations of right Leibniz algebras of dimension up to three over a field
$\mathbb{F}$, with $\operatorname{char}(\mathbb{F})\neq 2$. We describe the
main properties of such class of Leibniz algebras and we also compute the
biderivations of the four-dimensional Dieudonn\'e Leibniz algebra
$\mathfrak{d}_1$. Eventually we give an algorithm for finding derivations and
anti-derivations of a Leibniz algebra as pair of matrices with respect to a
fixed basis.
