In this note, we study the Yang–Mills bar connection
A 
, i.e., the curvature of
A 
obeys
\bar\partial_A^\astF_A^0,2 = 0 
, on a principal
G 
-bundle
P 
over a compact complex manifold
X 
. According to the Koszul–Malgrange criterion, any holomorphic structure on
P 
can be seen as a solution to this equation. Suppose that
G = SU(2) 
or
SO(3) 
and
X 
is a complex surface with
H^1(X,\mathbbZ_2) = 0 
. We then prove that the
(0,2) 
-part curvature of an irreducible Yang–Mills bar connection vanishes, i.e.,
(P,\bar\partial_A) 
is holomorphic.