  We consider generalization of the Cachazo-Svrcek-Witten (CSW) rules to
one-loop amplitudes of N=4 super Yang-Mills theory in a recently developed
holonomy formalism in twistor space. We first reconsider off-shell continuation
of the Lorentz-invariant Nair measure for the incorporation of loop integrals.
We then formulate an S-matrix functional for general amplitudes such that it
implements the CSW rules at quantum level. For one-loop MHV amplitudes, the
S-matrix functional correctly reproduces the analytic expressions obtained in
the Brandhuber-Spence-Travaglini (BST) method. Motivated by this result, we
propose a novel regularization scheme by use of an iterated-integral
representation of polylogarithms and obtain a set of new analytic expressions
for one-loop NMHV and N$^2$MHV amplitudes in a conjectural form. We also
briefly sketch how the extension to one-loop non-MHV amplitudes in general can
be carried out.
