  We consider a formulation of local special geometry in terms of Darboux
special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the
metric is obtained which is manifestly $\mathbf{Sp}(2n,\mathbb{R})$ covariant.
Unlike the rigid case the metric is not given by the Hessian of the real
function $S(P)$ which is the Legendre transform of the imaginary part of the
holomorphic prepotential. Rather it is given by an expression that contains
$S$, its Hessian and the conjugate momenta $S_I=\frac{\partial S}{\partial
P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional)
metric proportional to the Hessian with an appropriate conformal factor.
