  A new method for reconstruction of coronal magnetic fields as force-free
fields (FFFs) is presented. Our method employs poloidal and toroidal functions
to describe divergence-free magnetic fields. This magnetic field representation
naturally enables us to implement the boundary conditions at the photospheric
boundary, i.e., the normal magnetic field and the normal current density there,
in a straightforward manner. At the upper boundary of the corona, a
source-surface condition can be employed, which accommodates magnetic flux
imbalance at the bottom boundary. Although our iteration algorithm is inspired
by extant variational methods, it is non-variational and requires far fewer
iteration steps than most of them. The computational code based on our new
method is tested against the analytical FFF solutions by Titov & D\'{e}moulin
(1999). It is found to excel in reproducing a tightly wound flux rope, a bald
patch and quasi-separatrix layers with a hyperbolic flux tube.
