  A map $f$ from the quaternion skew field $H$ to itself, can also be thought
as a transformation $f:R^4 \to R^4$. In this manuscript, the Jacobian $J(f)$ of
$f$ is computed, in the case where $f$ is a quaternion polynomial. As a
consequence, the Cauchy-Riemman equations for $f$ are derived. It is also shown
that the Jacobian determinant of $f$ is non negative over $H$. The above
commensurates well with the theory of analytic functions of one complex
variable.
