  The usual form of the C-metric has the structure function
G(\xi)=1-\xi^2-2mA\xi^3, whose cubic nature can make calculations cumbersome,
especially when explicit expressions for its roots are required. In this paper,
we propose a new form of the C-metric, with the explicitly factorisable
structure function G(\xi)=(1-\xi^2)(1+2mA\xi). Although this form is related to
the usual one by a coordinate transformation, it has the advantage that its
roots are now trivial to write down. We show that this leads to potential
simplifications, for example, when casting the C-metric in Weyl coordinates.
These results also extend to the charged C-metric, whose structure function can
be written in the new form G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where
r_{\pm} are the usual locations of the horizons in the Reissner-Nordstrom
solution. As a by-product, we explicitly cast the extremally charged C-metric
in Weyl coordinates.
