  We numerically study the scaling behavior of period doublings at the
zero-coupling critical point in a four-dimensional volume-preserving map
consisting of two coupled area-preserving maps. In order to see the fine
structure of period doublings, we extend the simple one-term scaling law to a
two-term scaling law. Thus we find a new scaling factor $\delta_3$
$(=1.8505\dots)$ associated with scaling of the coupling parameter, in addition
to the previously known scaling factors $\delta_1$ $(=-8.7210\dots)$ and
$\delta_2$ $(=-4.4038\dots)$. These numerical results confirm the
renormalization results reported by Mao and Greene [Phys. Rev. A {\bf 35}, 3911
(1987)].
