  The purpose of this paper is to provide an octonionic description of the Lie
group $SL(2,{\mathbb O})$. The main result states that it can be obtained as a
free group generated by invertible and determinant preserving transformations
from $\mathfrak{h}_2({\mathbb O})$ onto itself. An interesting characterization
is given for the generators of $G_2$. Also, explicit isomorphisms are
constructed between the Lie algebras $\mathfrak{sl}(2,{\mathbb K})$, for
${\mathbb K}={\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$, and their
corresponding Lorentz algebras.
