  We take our first step toward getting finite results from the
alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory
techniques. Starting with the classical action of N=4 SYM with the leading
alpha'-corrections, we examine new divergence at one loop due to the presence
of the alpha'-terms. The new vertices do not introduce additional divergence to
the propagators or to the three-point correlators. However they do introduce
new divergence, e.g., to the scalar four-point function which should be
canceled by extra counter-terms. We expect that the counter-terms will appear
in the 1PI effective action that is obtained by considering the string annulus
diagram. We work out the structure of the divergence and comment on an
application to the anomalous dimension of the SYM operators in the context of
AdS/CFT.
