We review the algebraic structure of $mathbb{H}{sharp}$ and show that $mathbb{H}{sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $mathbb{H}{sharp}$ determines a rotation $R_{qp}:mathbb{H}{sharp}{ ightarrow}mathbb{H}{sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.