  We prove a regularity result for Green's functions that are associated to
elliptic second order divergence-type linear PDO's with coefficients in
C^{1,\alpha}(\bar{\Omega}). Here \alpha\in (0,1) and \Omega\subset \R^n is a
bounded C^{2,\alpha} domain in dimension n\ge 3. The regularity result gives
boundary estimates for derivatives up to order (2+\alpha) and, by using these
estimates, we extend the associated Green's operator to a globally defined
singular integral which of Calder\'on--Zygmund type.
