  We consider the loop equation in four-dimensional N=4 SYM, which is a
functional differential equation for the Wilson loop W(C) and expresses the
propagation and the interaction of the string C. Our W(C) consists of the
scalar and the gaugino fields as well as the gauge field. The loop C is
specified by six bosonic coordinates y^i(s) and two fermionic coordinates
\zeta(s) and \eta(s) besides the four-dimensional spacetime coordinates
x^\mu(s). We have successfully determined, to quadratic order in \zeta and
\eta, the parameters in W(C) and the loop differential operator so that the
equation of motion of SYM can be correctly reproduced to give the non-linear
term of W(C). We extract the most singular and linear part of our loop equation
and compare it with the Hamiltonian constraint of the string propagating on
AdS_5 \times S^5 background.
